For David Cameron there is a much more significant alliance than the one with Nick Clegg, a coming together that has defined his leadership from the beginning and will do so until the end. The alliance is not formal and never will be, but it is at the heart of his project as leader in a way the Liberal Democrats are not.

I am referring to the informal alliance between Cameron and Tony Blair, one that extends to some of those who worked closely on policy with the former Labour prime minister. The partnership started when Cameron as the new Conservative leader supported Blair's school reforms in 2006. Cameron went on to make the mischievous yet sincere observation that the Labour leader evidently wanted to go further and would do so if it were not for his wretched party and chancellor. The heir to Blair assured him that he would carry on with the reforms when he won a general election. He has done so.

The rapport goes well beyond two leaders. The Education Secretary, Michael Gove, a close ally of Cameron's, describes himself without irony as a Blairite. Famously he and others at the top of the Conservative Party regard Blair's memoirs as the equivalent of the Bible. Blair reciprocates. His interview in The Sun yesterday was reported as an endorsement of Cameron's policies and a warning to "Red Ed". The actual quotes were no different to those he had delivered in various broadcast interviews last week, but it does not take very much to present them as The Sun did. Blair appears to broadly support Cameron's public service reforms, and in his memoir argued in favour of George Osborne's contentious deficit-cutting strategy.

There are nuances. In a BBC interview, Blair stressed that his reforms were aimed at helping the poor, implying perhaps that Cameron's were not. But as Cameron makes the same emphasis, the nuance is narrow. In his Sun interview yesterday, Blair advises Miliband to be at "the cutting edge" and on the centre ground, without specifying what that actually means. Clearly he has in mind moving in the same direction as Cameron on several fronts.

The former prime minister is not alone. Blair's former policy adviser Andrew Adonis voted in favour of Michael Gove's school reforms. His former health minister Lord Warner appeared on the Today programme on Tuesday to put the case for the Coalition's original NHS changes, conveying more evangelical zeal than Andrew Lansley did when he launched his partially doomed revolution. On the World Tonight on Tuesday, there was an illuminating discussion between another former adviser to Blair, Julian Le Grand, and the former Lib Dem MP Evan Harris. Harris noted that Le Grand's arguments were so close to Lansley's he was surprised Blair's adviser did not support the original plans. Meanwhile two of Blair's former ministerial allies, Alan Milburn and John Hutton, have worked or work on specific projects for Cameron. Both have been known to tell friends: "These people are Blairites."

None of the interventions from some of the most pivotal figures in the New Labour era are malevolent or spurred by resentment. They are based on principled conviction, but that makes them more significant.

Cameron recognised that the key error of his predecessors was to oppose Blair and his allies, when politically, it was much more potent to support them. Again he did so, and does so, out of conviction as well as expediency.

As far as I can tell, Blair's commitment to Labour remains strong, as is the case of most of those aides and former ministers who put the case for Cameron's policies. Blair has behaved with characteristic dignity in managing the impossibly awkward role of a former leader, commenting rarely on British politics. But he applies his restraint widely. He chooses not to be critical of Cameron when invited to do so.

Whatever the motivation of Blair and others, the consequences are deep and underestimated. For Cameron, the Blairite glow of approval is like gold dust. Cameron's relationship with Clegg is obviously vital in providing the numbers that make a coalition possible. But Clegg is starting to stress the differences between the two ruling parties, a theme that will intensify. Some of Blair's former aides and ministers emphasise the common ground.

Although long ago Oliver Letwin had noted similarities between Clegg's politics and theirs, Cameron was less interested in the Lib Dem leader before last year's election. I am told he viewed Clegg with a degree of disdain. What has always mattered to Cameron is the implicit or overt backing of Blair and some of his followers.

In this context a significant moment in the saga of the NHS reforms arose when Alan Milburn expressed his concerns. Last autumn Cameron expected the usual dynamic to be in place, opposition from the Labour leadership and support from the likes of Blair and Milburn. When that support was not forthcoming, he knew he was in trouble. The degree to which he cares was demonstrated during Prime Minister's Questions yesterday when Cameron cited Blair three times as being in support of his policies. For a leader of a Conservative Party still not entirely decontaminated, it is a protective shield that is much more robust than that offered by Liberal Democrats. Parts of the Lib Dems oppose Cameron's reform programme with the same sincere conviction that attracts Blair and some of his followers.

While Cameron collects the gold dust, Ed Miliband is faced with a nightmare. It is one reason he is not making more headway. The battle over the NHS is a classic example. Miliband and others express their opposition, which is also sincere. Cameron responds by saying with total accuracy that Labour under Blair was following the same course in relation to the NHS. When Miliband and others argue against cutting the deficit too quickly, he and George Osborne are armed with quotes from Blair's memoir supporting them.

The reasons for the dynamic are complex and many. The wounds of the Blair/Brown era fester, and policymakers, bloodied by the battles, turn elsewhere for alliances. Some have moved to the right. Several of Cameron's policymakers inside No 10 are not easy to categorise and, in some cases, are not ideological even if he leads a government that historians will regard as being on the radical right. The Labour leadership opposes indiscriminately without defining clearly how it stands for more than the status quo, giving space to those excited by pure market-based reforms and a much smaller state.

The nuanced reasons are interesting but less important than the practical political consequences. As long as the informal alliance with Blair and some of his followers continues, Cameron is safe and Labour will struggle until it finds a way of addressing the issue. The policies that arise are a chaotic muddle, but for Cameron the political choreography is sublime.

s.richards@independent.co.uk;