Peter Mandelson came to the "Blair Years" class at King's College, London, yesterday, to talk to our Masters students. The required reading for this week was The Third Man, Lord Mandelson's memoir of his time as minister in Tony Blair's government, as European commissioner and as the surprise returner to the Cabinet under Gordon Brown in 2008.

He told the class that Blair as Prime Minister changed the country for the better while remaining unchanged himself:

Tony Blair maintained all his character, humour and balance throughout. He was unaffected by the pomposity of high office. What was nice about him was his self-criticalness, if that’s a word. He was aware that mistakes were being made, but he had a great self-correcting mechanism.

What did he do for the centre-left and for the country? For the centre-left he did nothing less than telling us how to be elected and how to govern the country again. He did so from what Roy Jenkins called the radical centre. Not as a party of class or sectional interest, but as a cross-class alliance of conscience and reform. The sort of party of the late Thirties and Forties, led by people such as Hugh Dalton and my grandfather [Herbert Morrison], and later Hugh Gaitskell. That is what Tony reinculcated into the party.

What he was seeking to do in creating New Labour was to set the goal of democratic equality – not of outcome but of opportunity – and a Fair Deal society.

Did the Blair government create this society? I would say overwhelmingly yes. The country is less divided, more socially inclusive, more socially mobile – a better society in my view. Poverty has been tackled. Public services were invested in and reformed.

As this was an academic seminar, however, Lord Mandelson said: "I want to dwell not on our achievements, which were considerable, but to ask: did we do everything right? No. I want to look at three areas where we could have done more or differently." These were the impact of globalisation, the "new politics" and Europe. On the first, he suggested that Blair had given too little weight to the problem of persistent inequality and the insecurities of those on middle incomes.

As for the "new politics" he accepted that Britain had not become much less centralised, and that "the realignment of the left, the progressive alliance, voting reform and state funding of parties" all failed to materialise. "Why? Because we overshot the runway in 1997. We did far too well for us and the Liberal Democrats to understand how much we could need each other."

He insisted that Blair's commitment to the realignment of the left, reuniting the Labour and Liberal traditions, was genuine rather than tactical. "It was his idea. It was what he thought would be his legacy." Similarly, he was fully committed to the pro-European cause:

Tony wanted a fundamental transformation of Britain’s relationship with Europe, with Britain and British leadership placed at the heart of the European project. That was derailed by George W Bush, by his response to 9/11, and his desire for regime change in Iraq. Chirac was hung out to dry: he was held responsible for the failure to get a second resolution.

You know Tony came into government believing very strongly in two pillars: the European and the American. He believed strongly in both. The problem was that George Bush presented him with a strategic choice – you’re either with us or them. And Tony believed it was of paramount importance not to allow the US to go it alone.

In questions, he was asked about his famous comment in 1998 about being "intensely relaxed" about people becoming filthy rich.

The CEO of Hewlett Packard, Lewis Platt, said to me, "Why should I consider investing in a country like Britain that’s now got a communist government?" And I said I was intensely relaxed about people becoming filthy rich, as long as they pay their taxes. That second part is often left out, usually by The Guardian.

What’s the lesson there? Never do irony.

Another student said: "Margaret Thatcher was asked what was her greatest achievement and said, 'Tony Blair.' Do you think Blair would say, 'David Cameron'?"

You’d have to ask him. He’d be entitled to. What he [Cameron] has done with his running mate, is to steal the centre ground from under our feet. Not just a national minimum wage but a National Living Wage, paid for out of higher productivity – we’ll see about whether that materialises.

Cameron and Osborne: I mean they just swallowed the entire manual. They didn’t just read the executive summary, they are following the whole thing to the letter.