In the end, what made the difference was a gesture so small that it could easily have been shrugged off or just plain forgotten.
Who, honestly, bothers to stand on the doorstep of their school or office to look out for a client or pupil when back inside there are calls to make, emails to answer and work to be done? What is the point? It is not as if anyone notices.
But Tracey Palmer noticed.
"I still remember like it was yesterday," says Ms Palmer, who has a three-year-old daughter, Caroline. "I remember walking down to the children's centre and feeling very hot and flustered. I was having second thoughts about whether to go in. I got closer and closer and I was thinking: 'Do I turn around? Do I go back? I don't really want to go.' Then I saw Debbie stood there. Seeing her made me feel it would be OK."
Ms Palmer was taken inside by Debbie Scrivener, one of the outreach workers based at the Leys Children's Centre, who had previously visited Ms Palmer in her home on the Blackbird Leys estate in Oxford. She was given a cup of tea and welcomed to a stay-and-play session.
"Caroline was about one year old," says Ms Palmer. "There were lots of soft toys which she thoroughly enjoyed and I met some other mums, so I kept coming and I'm still coming now."
It all seems straightforward: put on a stay-and-play, invite parents, sit back. But Ms Palmer could have slipped through the net if it was not for Ms Scrivener.
After all, this was not her first contact with the centre. Ms Palmer had been referred to a parenting programme, Oxpip, when Caroline was six months old. Ms Palmer's mum had died when she was just 18 months old and she needed reassurance in how to mother. She finished the programme, and that could have been it; she could have been ticked off as a parent contacted, a satisfied service user.
But instead, when that class ended, Ms Palmer was put in touch with Ms Scrivener.
"I had virtually no confidence and it was difficult for me to get out," Ms Palmer explains. "Debbie came to my house - I really appreciated that. It was she who said, 'Why not come to the centre?'"
And she did.
Jenny Martin, who has a background in social work, is the manager of Leys Children's Centre. To an outsider, the centre itself seems fairly harmless, converted from two nondescript 1930s brick-built semis with a sea-blue curved extension on the front. But for locals, its former life as a social services office meant it had a reputation that was far from nondescript.
"When we took on the family centre it was really stigmatised," says Ms Martin. "When I went to speak to people on the Leys (estate), they would say: 'I won't go in there; if I go in there I'll come out without my kids.' We have worked really hard to make it a local centre where everybody is welcome."
It opened in 2004 and is considered a success. The stay-and-play sessions have proved vital in bringing people into the centre and providing a meeting place. For some, that is all that is wanted, but the real value of children's centres is the trust that is built up over time through the accumulation of small gestures of kindness such as Ms Scrivener waiting by a door to greet newcomers.
And it was those kinds of relationships that were threatened earlier this year, when rumours of closure started to circle children's centres. They are the kind of rumours that have beset children's centres around the country since the Coalition came to power; rumours that have set off any number of local campaigns and newspaper stories.
Budget cuts, say doom-mongers, will mean an estimated 250 centres could close, according to a survey by the children's charities 4Children and the Daycare Trust. These rumours came as a shock to parents who had been assured by the coalition Government that Sure Start was safe in its hands.
In fact, Sure Start funding - the pot of cash used for children's centres - has remained the same at #163;1.1 billion a year. What has changed is the removal of a ring fence that meant it had to be spent on the centres themselves. Now local authorities have a single fund, the early intervention grant, for both the centres and other children's services, including free early-education places for disadvantaged two-year-olds, short breaks for disabled children and targeted support for vulnerable young people and families. Overall, this pot has shrunk from #163;2.5 billion to #163;2.2 billion a year.
It is this cut - and the corresponding reorganisation - that has really galvanised local campaigners.
Hampshire Save Our Children's Centres is one of a number of campaigning groups formed at the beginning of the year in response to the threatened cuts. It was founded by Catherine Ovenden and Kate Reynolds, a 32-year-old former teacher.
"A lot of our friends are teachers, and I was the first to have a baby out of the group and it was quite lonely," says Ms Reynolds, who has two children, Oscar, two, and Ottilie, one. "After I had Ottilie, I did suffer from postnatal depression. Because I already had a relationship with the staff at the (Windmill and Sails) centre and other people who used it, it was they who realised I wasn't in a very good place.
"I was not saying: 'I'm coming here because I have postnatal depression.' I was coming because my child wouldn't sleep. I would go to a group, the children play and an outreach worker circulates and somehow they teased the problems out.
"A family support worker came to the house and went through the options to address sleeping problems. It's good to have that relationship. I was in a really bad place after Ottilie - I couldn't leave the house," Ms Reynolds adds.
"So finding out Hampshire (council) was going to radically change the delivery and structure of the centres and services sort of got me fired up. I arranged a walk to one of the consultation days and through that I met Catherine Ovenden and we formed Hampshire Save Our Children's Centres."
In May, Hampshire said it would not close any of its 81 children's centres, but as funding has been reduced by 8 per cent it has proposed merging the management of a number of centres to reduce the number of "separate entities" to 53 - although all locations would remain open. The parents' campaign is now waiting to see how this will affect services.
Dr Margy Whalley is one of the country's leading early-years experts and founder of the National Association of Children's Centres. "In some areas, where councils threatened to close children's centres, there was an enormous fightback from parents, which has been amazing and powerful," she says. "For me, it was very exciting because it was really about early years growing up and saying, 'We are critical, you can't just close us on a whim.'"
And others support this notion. Cynthia Knight, manager of the St Thomas Children's Centre in Birmingham and a trainer for centre leaders, argues that the protests against possible closures prove that children's centres have come of age - they are not just in the community, but of the community.
"Parents are now aware of what they might lose," Ms Knight says. "I don't think our local councillors really understood the impact that has happened in terms of family experiences.
"What families need, centres provide. Parents here keep coming and they volunteer because they feel part of something which is local and accessible and where they will be treated with respect."
The money going to Birmingham for early intervention, including children's centres, has been cut by 15.9 per cent. But in April, the council announced it would not close children's centres or reduce services in them.
And the statistics suggest that this is the national picture, too - the country is not facing a wholesale cull of centres. As reported in last week's TES, while almost #163;96 million has been sliced from children's centres' funding, according to figures acquired from 133 councils - an undoubtedly painful cut of 10 per cent on average - the widespread closures widely predicted have not taken place.
But the storm has not entirely abated - a third of centres are under review, with many councils due to start consulting on their future this autumn. Evolution seems to be the order of the day. And it is not as if this is something new to the sector.
The forerunners to the Sure Start centres stretch back to at least the 1970s, when integrated centres brought together early education and childcare. Then, in 1999, this was formalised with the launch of the Sure Start Local Programmes as a service designed to provide holistic help to all pre-school children in the most disadvantaged areas of England. The best way to lift children out of poverty was to get parents into work, and Sure Start provided quality childcare linked to early education, job centres and adult-education classes. It also helped children and their families through parenting classes, stay-and-play sessions, health sessions and some specialist support such as speech and language therapy.
But there was a structural difficulty - half of the children in poverty lived outside the Sure Start areas. So, in 2004, the Labour government announced it would move towards a universal service and expand into more wealthy areas, although funding would not be at the same level because the need in these areas was not as great.
The drive to expand the centres to cover the country began in earnest in 2006, and over the following four years a mismatched web of large, small, new, old, refurbished and rebranded centres grew to cover the country. The network of 3,621 centres is now as large as the state secondary-school sector and as disparate as grocery shops. And some kind of universality has been achieved.
However, it is this drive to keep a universal service that has now led to concern about how the system will work with less cash. Indeed, some are predicting the development of "ghost" centres - those that offer fewer and fewer parenting classes and whose staff cover larger and larger areas. Critics are concerned that these centres will find it much harder to build the relationships that are the cornerstone of children's centre work.
Despite these warnings, the Government has insisted that children's centres will remain universal. David Cameron told the Conservative party conference in 2009 that "Sure Start will stay, and we'll improve it".
A month later, Mr Cameron added a little more detail. "For families, Sure Start should stay, but it must better involve voluntary bodies and charities and increase its focus on the poorest." Ministers have also suggested that a payment-by-results system should be introduced as a way of driving up outcomes while keeping down the cost to the taxpayer.
Perhaps surprisingly, Dr Whalley, who is also director of research at Pen Green Children's Centre and Research Base in Corby, Northamptonshire, says the plans are not without merit. "I'm largely optimistic," she says. "I think the fight-back in the past six months in local areas has been a very powerful indication that Sure Start centres did have an impact and local communities do feel people are able to have a voice in how services are run.
"But without ring-fencing we are vulnerable."
Back in Oxford, Tracey Palmer turns up at the Leys Children's Centre with her daughter. The family has now moved away from the area and, although there is a children's centre nearer to her new home, Ms Palmer has made friends here. So she makes the three-mile journey by bus.
She strolls into the cafe area, her thick, dark hair tied back. Relaxed and smiling, she takes Caroline's hand. "Come on," she says to her daughter. "Let's go and play."
LOST AND FOUND
Paula Mitty, 44, who lives on the Blackbird Leys estate in Oxford, was unaware she was "hard to reach". She has lived on the estate for 16 years and has four children - an 18-year-old daughter, a seven-year-old boy and six-year-old twin boys.
She is passionate about the help she has received from staff at the Leys Children's Centre in the past three years, during which time an abusive relationship with the boys' father unravelled.
Ms Mitty was first put in touch with the centre by a teacher at her son's nursery school, who suggested she tried its parenting course. She found the course had some great ideas for coping with small children's behaviour but was really for families without deeper issues. When she pointed this out she was put in touch with outreach worker Teresa Fieldwick, who helped her find support and advice.
"I rang Teresa one day, saying I just couldn't do it any more. She got to me in half an hour. They helped me become a totally different person."
The initial reaction of local authorities may have been to cut the "phase 3" centres - those in the wealthiest areas - in order to ensure enough cash for the centres serving the most deprived areas. But Ms Mitty's story shows that there are powerful arguments for a universal network.