Lord Adonis came to talk yesterday to the Masters students taking the "Blair Years" contemporary history module that I teach with Jon Davis at King's College, London. It was a fascinating dissection of radicalism versus caution and a fitting way to bring the course to an end.

He said that he joined the Labour Party in 1995, the day after Tony Blair succeeded in reforming Clause IV of the party's constitution (which committed it to the common ownership of the means of production). "That was when I decided that the liberals had achieved a reverse takeover of the Labour Party." He joined the Number 10 Policy Unit in 1997, becoming its head in 2001. In that role he started to set up academy schools, which he continued to do as schools minister in the House of Lords from 2005.

After Blair stood down in 2007 he was kept on by Gordon Brown and expanded the academy programme further. He moved to the Department of Transport to work on the High Speed 2 rail line in 2008 and joined the Cabinet as Transport Secretary 2009-10. He is now chair of the Government's Infrastructure Commission – and a visiting professor at King's.

His subject yesterday was the evolution of Blairism:

Political parties are largely franchise operations vested in leaders and their teams. The Labour Party of Harold Wilson was very different from that of Neil Kinnock, which was different from that of Tony Blair. The same is true of the Tories. Ideas matter but the relationship of ideas to leaders is vitally important. Jonathan Freedland once wrote that people believe in people who believe in ideas; they rarely believe in ideas themselves.

Tony was essentially a social liberal with a strong imperialist streak. He was strongly in favour of the assertion of power abroad. He was more Thatcherite than Thatcher; he was positively Gladstonian. Those ideas became more apparent over time. Equally, the extent of his liberalism was disguised in the early years because he used Labour language.

Tony wasn't wildly interested in policy. Policy tended to be franchised out to people he appointed. What he was very good at was stopping things happening, such as any threat to private schools or grammar schools.

He was only really interested in public services that affect the middle class. He never wanted to reform the police – the Tories would have to do that. He was not interested in local government, except in London, because of the middle class. And his interest in London rapidly waned when it became clear that the mayor was going to be Ken Livingstone. And he had no interest in repeating the changes in London elsewhere.

Health and education were the big public services the middle class consumed, and they were electorally and socially vital to his project. He wanted to make them more user-friendly to the middle class without upsetting the Labour Party. So his approach was to franchise policy increasingly to ministers who would be radical and then to row back.

After a cautious start with the first secretaries of state, Frank Dobson and David Blunkett, Blair "franchised" policy to people who would be bolder. In health, to Alan Milburn, who became Secretary of State in 1999, and in education to Adonis, although Blunkett was succeeded by Estelle Morris in 2001, who was appointed to try to keep the teacher unions on board.

Asked about Blair's regret in his 2005 speech that he had not been more radical ("Every time I've ever introduced a reform in government, I wish in retrospect I had gone further"), Adonis said: "He didn't regret it at the time, though."

Lord Adonis, a visiting professor at King's College, London, at yesterday's class

He described the origin of academies, which started in 2000 as a small experimental programme for failing schools, and the struggle to set a target for expanding the number, which had reached 200 by the end of Blair's time as Prime Minister. He wanted 500, Alan Johnson (Blair's last Education Secretary) offered 300. Blair decided on 400. Adonis was worried that "Gordon Brown might come in and tear it up", but "Gordon realised that academies were working, although he wouldn't say so publicly" because of the hostility towards them from parts of the Labour Party. Adonis realised Brown would back them "when one of his advisers came to me to ask how to get his son into Mossbourne" – Mossbourne being the outstandingly successful academy in Hackney whose head, Michael Wilshaw, is now head of Ofsted.

Lord Adonis said the combination of higher spending and reform on health and education produced results. It had to be remembered that in 1997 the NHS was "on the verge of becoming unviable", and that in the 13 years of Labour government "there was no increase in the proportion of children going to private schools, despite a huge increase in incomes".

On constitutional reform – devolution, House of Lords, Human Rights Act, Freedom of Information – "Tony did the minimum he could get away with, the minimum that was credible."

Where Blair was really bold and radical was in foreign policy, he said.

He was far bolder than anyone had attempted since Anthony Eden and than had been achieved since the Second World War. It was more radical conceptually than public service reform. On public service reform Tony was not very bold and [he was] successful. On foreign policy he was very bold and largely a failure.

He described early "liberal interventionism" in Kosovo and Sierra Leone as "essential", but "it was the post-9/11 world that changed it". He said: "Nobody would be talking about liberal interventionism if it was just Kosovo and Sierra Leone. It was Afghanistan and Iraq that made it big."

Asked if he thought Blair was a good Prime Minister, he said: "Yes. He left the country in a better state than he found it, but its international reputation was worse."

Asked about Blair's failure to promote possible successors other than Brown, Adonis said:

The only alternative leader who was recognisably viable was David Miliband. Tony did almost nothing for him. He didn't make him Foreign Secretary in 2006, appointing Margaret Beckett instead. He'd done a deal with Gordon – promoting David would have been seen as a seriously hostile act.

Lord Adonis said he didn't think Blair would ever have moved against Brown.

He constantly licensed people to talk about a government without Gordon but never showed any inclination to move. Someone said they couldn't imagine the conversation in which he sacked Gordon, which I think is right.

Asked about the failure of Labour-Liberal Democrat co-operation in 1997-98, he said that was "impossible" because of the size of the majority, and that Blair "never had any intention" of implementing Roy Jenkins's plans for electoral reform.

The great missed opportunity in Lib-Labbery was not under Tony but under Gordon. Gordon could have made a bigger break on Iraq. He did promise the Alternative Vote in the manifesto, but he seemed to want to do it without ever talking to the Liberal Democrats.