Labour had been urged to sack Damian McBride, Gordon Brown’s controversial former spin doctor, over allegations that he has been secretly helping the Leave campaign.

Mr McBride, who now works for shadow Defence Secretary Emily Thornberry, accidentally posted a private message on Twitter that appeared to show him advising Tory cabinet minister Michael Gove.

The spin doctor, who was sacked by Mr Brown, posted the message which read: “V good! BTW, I'll email you another VAT-related idea this evening. Just in case there's a day/interview where MG is looking for a new line.”

The tweet has led to suspicions that it was Mr McBride who was behind an announcement by Vote Leave last week that Brexit would allow the Government to cut the rate of VAT on fuel in order to reduce energy bills.

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Nick Herbert, the head of the Conservative Remain campaign, has now written to both Mr Gove and Ms Thornberry demanding they explain what role Mr McBride was playing in the Leave campaign.

“Are you able to clarify precisely what contact Vote Leave staff have had with Damian McBride since your campaign launched?” Mr Herbert wrote to Mr Gove. “I feel sure that, given Damian McBride’s history of personal smears and underhand tactics against Conservative Party MPs, you would want to disassociate yourself and your campaign from him.”

In his letter to Ms Thornberry, he wrote: “You and I disagree on many things, but we are united in our support for Britain remaining in the European Union.

“I am sure that you will be abhorred by any suggestion that Damian McBride is advising Vote Leave whilst in your employment. As the official Labour Party policy is to remain in the EU, Damian McBride should of course respect that. I ask that you urgently investigate this matter and immediately terminate his employment if any wrongdoing is found.”

Mr McBride is thought to have been consulted because he is a VAT expert. He has not announced his support for the Leave campaign and as a senior advisor to Mr Corbyn's team would be expected to back remain or stay neutral on the issue.

Vote Leave said reports that Mr McBride is advising it on policy were “completely untrue”.