"Two weeks' paternity leave in two days," he jokes. Alanna is his third daughter and hasn't left hospital yet. Grant, 45, is a Scouser transplanted to what locals call the Wild East, but he recognises the landscape: white working-class territory, inner-city sink estates on the edge of London. Nobody feels they're sharing the capital's wealth here. The community still seems stunned by the winding down of Ford's motorworks.
The school is ringed by tower blocks. Teachers call the slip road into the upper building "sniper alley". Old hands say that before Grant took over in 1997 skinheads ran the school.
"Gang warfare, drugs, violence, graffiti - the place was completely out of control," Malcolm Allcroft, Clack's social inclusion manager, says.
"Teachers were abused physically and verbally. I fought in the first Gulf War, and I'd rather have been in my tank fighting in Basra than here. It was unreal."
The local paper, which now celebrates each Robert Clack soccer win and exam record, took a dim view, with good cause: the pupils once torched reporters' cars.
That has all changed thanks in part to a few basic measures: a rigorously implemented discipline code, school uniform (blazers, no sweatshirts), a short, sharp burst of 100 fixed-term exclusions, a big expansion of sport and arts ("our drugs policy"), and a serious investment in care for disruptive or disturbed pupils.
Robert Clack has its own referral unit, where teachers send those who disrupt lessons, and a learning support centre for those with longer-term problems. It's expensive but successful.
And while Grant welcomes the new leadership incentive grant, you suspect that he thinks it could be better spent on more practical measures - particularly with a pound;200,000 hole in his school budget this year.
It seems a traditional view of leadership - the charismatic head, leading from the front, carrying the school forward on the strength of his vision, his personality. He's a big bloke, a real physical presence in the school and in the community.
Grant says what he did "isn't rocket science", but it did require commitment. A thread runs through his conversation: responsibility. He has a responsibility to the kids, to their parents, to his teachers. He decided every exclusion personally, and met all the parents, even if shift patterns or bloody-mindedness meant they would only see him at 10pm or 6am.
But he is no less responsible to the people of Dagenham. "I didn't realise how important the school was to the community until I met the parents," he says. He has to be there for them.
Hence the buses: "I stopped five or six outside Safeway, introduced myself to the driver and the passengers. They looked at me like I'd been let loose from an institution. I said: 'Here's my number - if there's any trouble with our pupils, get in touch.' " He rode with the kids on the top deck; the news went all round the community. "People don't expect you to solve all society's problems," he says, "but they expect you to have a good crack."
Clack's sports director Barry Taylor appreciates his boss's strengths. "It takes a strong character to run a school like this and there aren't many like Paul," he says. "If he leaves, we could struggle. Even with all the systems in place."
Nevertheless, staff say Grant is an inclusive leader who gives them independence and a firm contribution to policy. He turned the school round without sacking anyone, has invested in middle, not senior management, and regularly promotes from within. Two deputies have won headships.
Teachers still recall his first staffroom speech. Malcom Allcroft remembers it well. "He said: 'Please believe in me'."
Grant explains his position. "I made sure the agenda I set out was the colleagues' agenda, because my first job was to restore their morale."
Paul Grant sits in on all the school committees and heads of department meetings, "to support them".
Might it be inhibiting? "Those are always line calls. You can be called an absentee landlord or too intrusive. Hopefully, I'm neither."
He adds: "Schools where people's confidence has been shaken need a certain type of leadership. There will be scenarios that you can train people up for, but in our society, some people believe the buck stops with the head."
Grant takes pleasure in mocking fancy management theories and time-wasting consultants. In fact, he's up on all of them - he has an MA in education management and says he can talk theory all day if he wants.
And it's not all about charisma. Improvements are rooted in concrete policies: the behaviour system; a template for well-structured lessons; a weekly half-hour of quiet reading for pupils and teachers; regular monitoring of students' bookwork.
Grant says the incentive grant offers a chance to expand his tiny leadership team, bring on future leaders and consolidate progress. But on collaboration, the Government's keenest hope for the grant, he's cautious.
Such a small leadership team doesn't leave much slack - but then that assumes collaboration starts at the top.
Even as he applied for the job, Grant didn't aspire to headship; he had, he says, typically working-class low aspirations. Perhaps he surprised himself - and is now making it his mission to ensure his pupils do the same.