Owen Jones: It's time to demolish the myth about Tony Blair

You will struggle to find more devout supporters of Tony Blair than those at the top of the Conservative leadership. "I can't hold it back any more; I love Tony!" Michael Gove once exclaimed. David Cameron famously described himself as "the heir to Blair", and senior Tories refer to him as "The Master". "His influence is very firmly felt," a senior Tory told The Times. "He's like the footballer Cristiano Ronaldo – gone but still greatly admired." Screaming teenagers at Take That concerts in the mid-1990s come to mind.

As Blair took to the Leveson Inquiry this week, his admirers went a bit weak at the knees. Blair is certainly an exceptional public performer: indeed, he is something of a natural. When he was at the public school Fettes, teachers described him as "a complete pain in the backside", but he excelled at acting. Along with Cameron, he is rare among British Prime Ministers for his polished charisma; although, unlike the current Tory occupant of No 10, he never looks like an artery risks bursting when he is under fire.

But the Tories really love Blair not because of his undoubted political skills, but because they think he was "one of us", albeit trapped by the Labour Party. In his first joust with Blair after taking over as Conservative leader, Cameron offered to support him against his own party over his policy of marketising comprehensive education. "With our support, the Prime Minister knows there is no danger of losing these education reforms in a Parliamentary vote," Cameron crooned, mocking Labour backbenchers. "So he can afford to be as bold as he wants to be." And, in reality, Labour's current opposition to what the Coalition is doing is hobbled by the fact that Blair laid the foundation for so much of it.

Take the privatisation of the NHS. Under Blair, private sector involvement began to flourish and a commercial directorate was set up in the Department of Health. Gove is now expanding Blair's Academy schools programme, and free schools are a logical extension of them. The Coalition trebled the tuition fees that Blair introduced. Across public services, Blair expanded the role of the private sector – though not as fast as he would have liked, thanks to internal party opposition. But Cameron is taking this "reform" (the Blairite and Tory code word for "privatisation") ever further. "Public sector reform" has come up in the many conversations Blair has apparently had with Cameron, and I'm sure the ex-PM has had much advice to offer.

In his memoirs, Blair effectively backed Cameron's cuts programme, and argued that Conservatives would "be at their best when they are allowed to get on with it – as with reforms in education". "They will be at their worst" not when their cuts would be hammering communities Labour exists to represent – but rather when they were first to compromise with "the Old Labour instincts of the Lib Dems". If we were to define "Cameronism", it would surely be Blairism liberated from the shackles of the Labour Party.

Unlike Clement Attlee and Margaret Thatcher, Blair failed to establish a new political consensus. He accepted the fundamentals of the Thatcher settlement: low taxes on the wealthy, weak trade unions, the dominance of the market over all. His great departure from Thatcherism was a desperately needed boost to spending on public services. Nothing remains of this as a principle in British politics. It is left to arch-critics of Blair like myself to defend a big chunk of his government's economic record from his own supporters. And contrast how the poorest fared with previous Labour governments. Four years before the crash, the income of the bottom third began declining. Under the Labour governments of the 1960s – which Blair delighted in defining himself against – the poorest 10 per cent saw their real incomes surge by 26 per cent, compared with a 16 per cent rise in median incomes.

It was the murderous invasion of Iraq – described by former UN Secretary-General Kofi Annan as "illegal" – that, for many, makes Blair unforgivable rather than a mere disappointment. It competes with the expenses scandal for the damage it did to faith in politicians. While in power, he courted despots like Egypt's Hosni Mubarak, whom he described as "immensely courageous and a force for good" when the Egyptian people rose against him. Today, the man who partly justified the invasion of Iraq with Saddam's sickening human rights record is being paid $13 million to advise the brutal dictator of Kazakhstan.

His defenders argue that Labour could not have won without him. It is a myth. Black Wednesday in 1992 finished off the Tories, and Labour enjoyed subsequent massive poll leads under John Smith. Of the five million votes that Labour lost in its 13 years in power, four million went awol under Blair's leadership. It wasn't so-called "Middle England" that deserted the party. According to Ipsos MORI, while middle-class professional support for Labour declined by five percentage points between 1997 and 2010, support among skilled workers plummeted by 21 per cent.

His influence is certainly "very firmly felt" among his adoring Tory fans, as they build on the foundations he laid. But Labour's leaders would be best advised to leave the swooning to Cameron's acolytes. Blair was fortunate to lead Labour just as Tory Britain imploded; but the old Blairite formula offers nothing to those who want a real alternative to the Conservative crusade.