At Cambridge, you get used to feeling like you haven’t done enough with your time; rubbing shoulders with students who spent their years out building wells for poor kids in places we haven’t heard of is a regularity. If anything, I am even more irked than most by this sense of guilt, so I had to brace myself before meeting Brett Wigdortz.

A brief biography: after studying at Richmond and obtaining an MA from Hawaii, Wigdortz went on to work as a Programme Officer at the Asia Society in New York City, then as a journalist in Asia. He then had a stint as a researcher at the East-West Centre in Honolulu. After this, Wigdortz joined McKinsey & Co., working as a consultant in Indonesia, Singapore, Manila and London. Most importantly, Wigdortz founded Teach First.

My nerves are misplaced. Wigdortz is laid back and affable; not at all put out by the horrendously small and dull room I’ve managed to secure for our interview. I begin, compelled by envy for his résumé, by asking Wigdortz what motivated him back in 2002 to give up his consulting career and start Teach First. “When I was at McKinsey, I became involved with a project which was looking at how businesses could help education in London,” he begins.

“And I quickly learnt two different things. The first was that in England the biggest determinant of a child’s success at school is how rich their parents are – in fact, the correlation between those two factors is worse in England than any other OECD country. If you estimate the parental income of a kid here, you can usually estimate what their GCSE results are going to be.

“The second thing I learnt was that if you could get children from a poorer background excellent teaching and excellent school leadership then they would do just as well as children from wealthier backgrounds. I felt like this was something that could make a real impact – more than some of the other things I’d done in the past. So I left McKinsey permanently to pursue it.”

This matter of fact account of events doesn’t quite do justice to the scale of the achievement. Last year, Teach First placed 485 of the country’s top graduates into 219 of the country’s worst schools. This year they’re aiming for 650 graduates, who will be trained for just six weeks before being sent into inner-city comprehensives.

Yet I noted potential problems in the Teach First philosophy. Teach First is largely financed by a group of corporate graduate employers who take a keen interest in the leadership skills graduates develop during their teaching. I ask Wigdortz if it’s sound policy to incentivise graduates into teaching with opportunities in the corporate private sector.

“Our teachers work really hard for two years to raise the aspirations of the kids they’re working with – if after that they want to move on to Proctor & Gamble that’s fine. What we’re trying to do is to create a ‘mafia’ whose focus is addressing educational disadvantage – we call these people ambassadors. We have about 50 working for Deloitte now, and almost all of them are doing things like mentoring kids, and acting as school governors.”

From this I point out an irony in Teach First’s philosophy, in that it recruits a ‘mafia’ of privileged high-fliers to address social disadvantage. It’s clear before I finish talking that Wigdortz doesn’t agree. “I disagree with the term privileged – we have a lot of Teach First applicants who were taught by Teach First. Sure, they’ve been successful and went to good universities; but you want the best leaders to teach kids. Every organization in the country wants the best leaders; we think the best leaders should work with the kids from the poorest backgrounds.”

Presumably, then, Teach First are in favour of David Cameron’s recent announcement to make teaching a “brazenly elitist” profession? Cameron has pledged to cut funding for teaching applicants with lower than a 2:2 degree. Again Wigdortz doesn’t agree: “Teaching shouldn’t be brazenly elitist in an academic sense. Those who get the best grades aren’t the best teachers and we certainly don’t look for that. Though in many ways if you rule out people with a third you’re actually only cutting out about five or ten percent of graduates.” Something of a futile gesture on Cameron’s part, perhaps.

We move on to talk about Britain’s education system as a whole. “I’ve been to enough schools and seen enough kids to know that the British education system is failing some kids,” Wigdortz asserts, “it’s not a push to say that. Some of the saddest things I’ve seen were when I went to a school six or seven years ago and it was clear that not many good things were happening.

“Having gone back there now and seen the schools with a new head teacher and some other new teachers, they’ve completely changed, which is really exciting but also depressing. The kids haven’t really changed from seven years ago, where they live hasn’t changed: it’s just the teachers that have changed.”

Wigdortz’s eyes dash to the clock on his iPhone so I know my time is almost up. As happens increasingly often these days, Lord Mandelson is brought into the conversation. What of his comments that elite universities aren’t doing enough for the working-class? Taking some time to think, Wigdortz answers, “I almost always hear from Cambridge graduates at Teach First that they are teaching kids who are more intelligent than the people they went to Cambridge with.

“Over 50% of Cambridge’s new intake this year were privately schooled, there is no way that half of the smartest people in this country went to private school. Lots of talented kids at comprehensives do really well in school but they don’t know how to apply to university and they think it’s too expensive. To them it’s like people at Cambridge have three eyes and green skin.”

Wigdortz’s zeal is infectious, but it is his acute awareness which will make Teach First a formidable force in the future of education.