There is a secret club at the centre of British politics. Numbering no more than 15 frontline politicians and a similar number of key advisers, it includes the last remaining Blairites and the "Cameroon" Conservatives and "Orange Book" Lib Dems at the top of the coalition government. Its members, divided by tribe, are bound by a truth they dare not admit – that they have far more in common with each other than with their own parties. What is more, by the time of the next election they will have run Britain for 15 out of 18 years, the only interruption coming when Gordon Brown departed, to his cost, from the modernising path that Tony Blair beat and which David Cameron and Nick Clegg are now following.

The fact that all three groups are vastly outnumbered within their own parties explains both why they are attracted to the idea of political realignment and why that idea never comes to anything. When a member of Cameron's wider circle told journalists recently he would like to see the coalition extended beyond the next election – even if his party were to achieve a majority in the Commons – Tory activists were up in arms, accusing the leadership of a secret plan to "castrate the Tory right". Fifteen years ago similar plans and similarly enraged responses were emanating from the Labour party as Blair plotted with Paddy Ashdown to bring the Lib Dems into his first-term government.

Blair's plan was logical enough. By co-opting the Lib Dems he hoped to buttress his administration with a number of like-minded, centrist politicians who could help deliver his reform agenda while providing a bulwark against his own left wing. Today, many Conservatives are convinced their own leader has the same vision, albeit in mirror image.

It would be a mistake to think these modernising factions are united only in their exasperation with their parties' backwoodsmen. They are also bound by an extraordinary degree of political agreement which no amount of blue-, red- or yellow-wash can conceal.

Consider the ease with which the Lib Dems and Conservative leaderships put together a radical coalition agreement. Or the extent to which that agreement builds on the agenda pursued by the Blairites in their second and third terms. "Reform" in welfare, schools, higher education funding and the NHS – as Blair himself has recognised, each represents an attempt to complete New Labour's unfinished business.

What defines these politicians and separates them from their party colleagues, however, is a talent for alchemy, for taking base metals from left and right and turning them into political gold. Where the left has always owned the values of equality and social justice, and the right of liberty and aspiration, the modernisers have sought to blend the two.

To compensate for their party's historical weaknesses they tend to send contrasting signals; the Blairites and Orange Bookers emphasising their economic liberalism (a commitment to entrepreneurialism and wealth creation) and the Cameroons their social liberalism (tolerance and compassion). But in each case the audience is the same: moderate voters unconvinced by the partial solutions traditionally on offer.

What Blair never succeeded in doing was coming up with a name that captured the full vitality of his world view – thus allowing his critics to present it as a product of electoral calculation. In two recent political trends, set in motion by Philip Blond's book Red Tory and Maurice Glasman's Blue Labour, many see parallels with Blair's modernising mix of left and right thinking. But the nostalgic communitarianism at the heart of both leaves the modernisers cold: "We won't win with a Labour equivalent of warm beer and old maids bicycling," was Blair's dismissive response.

Though they may find it hard to admit, the creed that really unites these modernisers is liberalism. Cameron describes himself as a "liberal Conservative", while Clegg is that equally rare thing, a liberal Lib Dem. Even Blair now concedes that he considers himself a liberal on everything but law and order.

There is, however, a pragmatic reason why only a few of these liberals are to be found among the Lib Dems. It is that while they all aspire to occupy the liberal centre, most have realised this most fought-over piece of political real estate is only of value if it marks the end – rather than start – of your journey. Travel there from the left or right, and you will land in No 10. But start from the centre and try to work your way outwards and you are in for endless trouble as your party argues about which way to go and your enemies wait, ready to ambush you, on both sides.

Clegg's predicament illustrates the point. To critics on the left he is a Trojan horse for a cohort of Thatcherite ideologues hell-bent on shrinking the state. To those on the right he is the man in the way, a block on their ambitions. He can't, of course, be both. In truth he is neither. Clegg is a modernising politician who understands why people have turned away from state socialism and laissez-faire Thatcherism. Unlike Cameron and Blair, he made the schoolboy error of thinking the best place for an ambitious liberal politician was in the Liberal party.