Danny Alexander has ruled out further cuts in the 45p top rate of tax, even as Boris Johnson, the Conservative mayor of London, suggests such a policy will be in the next Tory manifesto.

Writing in the Daily Mirror, the Treasury chief secretary said he would allow his coalition partners to cut the highest rate of income tax “over my dead body”, reigniting a long-simmering tax row within the cabinet.

Mr Alexander added: “The top rate of tax has been an issue of late. Labour wants to take it back up to 50p, I think the 45p rate is the right place to be. I wouldn’t go to cutting below 45p – that would happen over my dead body. It’s better to say we are going to stick where we are.”

David Cameron has refused to rule out cutting the top rate to 40p, having already reduced it from 50p earlier in the parliament. So far, the Liberal Democrats have said they will back the prime minister’s plans, but only if he backs a tax on properties worth over £2m in return, something he has previously vetoed.

Mr Alexander’s comments now rule out such a compromise being struck, in effect guaranteeing that the top income tax rate will not change until after the 2015 election.

The Tories are likely however to include a pledge to cut the rate to 40p in their next manifesto, Mr Johnson later suggested. Speaking to the BBC’s Today programme, the London mayor said: “I don’t think it is reasonable always to keep UK tax rates higher than those of competitor countries.

“UK income tax is now higher than the average in the EU; that never used to be the case, I don’t see why that should be the case for the long term and I don’t see any reason why we shouldn’t bring it down.”

The spat is yet another example of the Lib Dems’ increasing willingness to pick fights with their coalition colleagues as they try to win back leftwing votes from Labour.

It comes just a day after the Financial Times revealed that the party had blocked an attempt by Eric Pickles, the Conservative local government secretary, to reduce the amount by which councils are able to raise tax. Mr Pickles had wanted to force any authority wanting to raise council tax by 1.5 per cent or more to hold a referendum to approve their plans, a decrease from the current level of 2 per cent.

But with support from Theresa May, the home secretary, Liberal Democrat ministers blocked the proposals, arguing local government was already struggling to cope with the scale of government cuts.

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