As Zac Goldsmith lags behind Sadiq Khan in the polls ahead of the London mayoral election, it's a case of all hands on deck in order to boost his chances come polling day. However, while David Cameron used PMQs last week to do exactly this -- attacking Sadiq Khan for his links to extremists -- the Prime Minister has still failed to convince members of his inner circle that Goldsmith is the man for the job.

After Cameron's sister-in-law Emily Sheffield appeared to get behind Sadiq Khan's campaign earlier this month, one of Cameron's closest friends has today declared that she won't be bothering to vote in the mayoral election. Writing in her Times column, Alice Thomson says she can't bring herself to vote for either candidate. Where Khan appears to lack principles, she says Goldsmith 'doesn't look as if he cares whether he wins or not':

“ 'Goldsmith should be the obvious alternative. But if Khan is a man who desperately wants the job but has few principles, Goldsmith is encumbered by many principles but fails to convince us that he wants to be in City Hall. The Tory MP for Richmond Park is telegenic, socially liberal and fiercely independent. He has never deviated from his determination to oppose a third runway at Heathrow.

His wealthy father founded the Eurosceptic Referendum party so he should have campaigning in his blood but this self-effacing, apologetic “white male Etonian” doesn’t look as if he cares whether he wins or not.'

While Thomson cites problems with both candidates, her criticism of Goldsmith is particularly curious given that she counts Cameron as a close friend and is seen to be a Conservative supporter. During the Leveson inquiry, Thomson was included in the six journalists the PM said he met so often that it would not be possible to list each occasion in the parliamentary register of meetings with newspaper executives:

“ 'There's a small number of journalists who are close friends of mine and who I see so frequently that I have not included them systematically in these lists, namely Daniel Finkelstein, Alice Thomson and Sarah Vine from the Times, Xan Smiley and Christopher Lockwood from the Economist, and Robert Hardman from the Daily Mail.'

If Cameron is unable to persuade one of his closest friends of Goldsmith's positives, then Zac's campaign is in deeper trouble than anyone first realised.