The view has long been widespread among commentators that Tony Blair is unusual: not exactly a Tory, but somewhere much closer to a continental Christian Democrat than a typical Labour Party product. James Callaghan reportedly said of him: "I don't know what that young man is, but, whatever he is, it isn't Labour."
Of course, while truth in advertising is laudable, renaming the party to the "Christian Democrats" would alienate voters of other faiths. Perhaps "Abrahamic Democrats" would be more appropriate, or (to include Hindus and such) "Theist Democrats"? That leaves the atheists out in the cold, of course, but everybody knows that they're amoral nihilists and shouldn't be encouraged.
In the cause of trying to contrive meaningful differences with Mr Blair, the Tories have opposed policies which, intellectually, they should support, while adopting inconsistent tactical postures. The frustrated search for territory beyond the Blairite shadow took the Tory election campaign to the wasteland of HIV testing for immigrants, strict quotas for asylum-seekers and a crackdown on gypsies, while saying little about the economy, hospitals or schools.And while Labour's transformation into Tories-with-good-PR has alienated a lot of leftists (many traditional Labour supporters didn't bother voting in the last election), it has been popular with elsewhere: 70% of current Labour voters regard themselves as "supporters of new Labour not old Labour".