Stateless and penniless, she could only speak a few words of English and had left her beloved parents behind her. The persecution of the Jews meant that she had already lived in seven different countries.
Steve has little time for intolerant politicians who impose restrictions on welfare benefits and training for the 25,000 who continue to reach out to Britain - most of them fleeing repressive regimes. Help them now and they will help Britain in return, she insists.
And she is a living example. Now aged 63, she is a multimillionaire and one of this country's most successful businesswomen. But she has never forgotten those early years, and was the perfect choice last week to launch the Refugee Training Partnership.
The project is led by the Central London and the City and Inner London Training and Enterprise Councils and the Refugee Council. It will provide training for refugees and asylum seekers to help them obtain work and qualifications for a career in the United Kingdom.
"My background has enabled me to understand the importance of freedom, not just freedom from poverty and from want. I am streetwise and independent. I want to make things happen, rather than let things happen to me. I am determined to manage my own life," says the woman who lists "sleep" as her recreation in Who's Who.
But real security comes from employability, and that comes from training, she added. "My interest in learning and training is partly genetic - I never stop learning. I like to know how I can earn my own way. I have skills that are wanted and if I cannot find a job at least I can find a customer to buy them," she said.
Steve's first refuge was with the Quaker movement which found a childless couple to foster her and her 10-year-old sister. The couple brought up the girls as their own. Steve's confidence and English skills grew quickly, she went to state school and got her first job at 18 as a scientific assistant with the Civil Service, "a glorified mathematical clerk", as she describes it. She studied in the evenings to gain a maths degree from the University of London.
Like many refugees, she grew to feel more English than the English, though she still felt damaged by her past and had, she remembers, an enormous chip on her shoulder. She was prickly, aggressive, "what the Americans call lippy."
The traumas of being a refugee and asylum seeker take years to overcome and these personal emotional battles are not easily won, but the Refugee Partnership will offer practical help - training in English, open learning support for IT skills, continued language support and help developing job-search skills. Careers officers will give free, confidential advice. The long-term aim is to have local partnerships self-financed with community support. "I wish something like this had been available when I was a refugee, " Steve said.
She has no time for critics who balk at public cash being spent by TECs on such initiatives. She was a founder architect of the TEC movement in the late 1980s and asks: "Who else? There is no one else but the TECs."
Colleges remain big providers but their efforts have been seriously hit by Home Secretary Michael Howard's crack-down on alleged scroungers. New benefits rules which followed closed the doors on many asylum-seekers - in some colleges one in 10 students was seeking asylum - before the exodus which followed.
She became Steve Shirley on marrying a physicist and remembers the "shock and horror" of others when she said she was determined to keep working after the family they were planning came along.
At 30, she started a software computer company with Pounds 6,000 capital - enough to pay for a portable typewriter and some stationery. Her husband Derek suggested that if she really wanted to succeed in such a male-dominated world, she should change her name from Stephanie to Steve.
Soon, she was inundated with letters from other women who also wanted to combine working with raising a family. They wanted to work for the intellectual stimulus rather than the money.
"Women at work were not taken seriously then. Perhaps running a little hat shop, but no more. I felt very lonely and isolated. But at the company, we worked as a team, not as me the employer and them the workers. That seeded the idea of empowering the staff through ownership."
She pioneered co-ownership, using a trust to hold shares on behalf of the staff. At one time, all her staff were women, many working from home or with flexible working conditions.
The company, the FI Group, was valued at Pounds 70m when it was floated on the Stock Exchange last year. About half (48 per cent) of the company is owned by the staff, very unusual for a publicly-quoted company. Some are now millionaires. Steve herself - for 25 years chief executive, now life president - is worth Pounds 35 million.
"It happened because nobody told me I could not do it my way. We took risks and worked hard. My example shows that you do not have to be stuck in the situation life puts you in. And training is what gets you out of it. It is very hard to get out of the poverty trap if you are illiterate and cannot seek new skills.
"Many of the wealth creators in Britain are refugees, outsiders who seek to reach for their own control. People need considered help to get them into the workforce and then they can do their own thing.
"We do not want refugees to join the underclass. It is very easy for a family without money or friends, sitting on someone else's floor, to slide down the economic spiral."