A man heads towards a polling station to vote in London. Ameet Gill, who served as the former prime minister’s director of strategy, said the Brexiteers’ commitment to leaving the free-trade bloc was the key issue of the campaign | Dan Kitwood/Getty Images Brexit vote was about single market, says Cameron adviser Remain campaign strategist said it’s ‘a bit weird’ to claim Theresa May doesn’t have a mandate to leave the single market.

LONDON – Leaving the European single market was “the instruction from the referendum,” according to one of David Cameron’s closest advisers.

Ameet Gill, who served as the former prime minister’s director of strategy until earlier this year and campaigned for a Remain vote, said the Brexiteers’ commitment to leaving the free-trade bloc was the key issue of the campaign and Downing Street spent “months trying to hang that round Leave’s neck.”

He said it was “a bit weird” for Labour and the Liberal Democrats to now claim that Prime Minister Theresa May doesn't have a mandate for a "hard" Brexit outside the single market.

Gill spoke to POLITICO from his new office in Brick Lane, east London, where he set up the political strategy firm Hanbury Strategy with former Brexit rival Paul Stephenson, a key player in the campaign to take Britain out of the EU.

The pair chose opposite sides in the Tory civil war over Brexit, but have now joined forces to shape the peace, advising companies how to handle the sweeping changes which are about to convulse British politics.

While still at odds over Brexit, they are adamant about one thing: Theresa May is winning and Britain will leave the single market.

Gill is particularly damning about the attempt to rewrite the history of the campaign by those who, like him, supported a vote to Remain.

“I remember in the campaign, the most significant moment of the campaign that we saw on the Remain side was in mid-April when Michael [Gove] made that speech saying we’re going to leave the single market," he said, referring to Cameron's justice secretary, a prominent Leave campaigner.

“Now, we spent the next three months trying to hang that round Leave’s neck. We went round saying, 'Look, a vote to leave is a vote to leave the single market.' So I do find it a bit weird with some politicians coming now saying that was never on the ballot paper."

Gill’s intervention serves as a reminder of the lengths to which the Remain campaign went to highlight the threat to Britain’s single market membership from leaving the EU.

Labour’s Brexit spokesman Keir Starmer emphatically rejects Gill’s claim. “There was only one question on the ballot paper — whether you wanted to vote to stay or to go," Starmer said. "The Conservative Party manifesto said nothing about the terms of exit if the vote was to leave. Absolutely nothing.”

He added: “Lots of people have made the point that this was one of the things being discussed in the campaign. That doesn’t turn it into a mandate."

Both Gill and Stephenson now anticipate a "hard" Brexit with a clean break from the single market.

“Markets are now starting to understand that fundamentally the reason the referendum was called in the first place was a political decision, not an economic one," Stephenson said. "Economically this is a very important event, but economics won’t necessarily be the primary driver of what is the deal."

Stephenson contrasted the discussion in Brussels about the political implications of any deal with the U.K. with the "proxy war" still gripping Westminster.

“It’s our belief that Theresa May sees a big opportunity, rightly, to connect with a whole bunch of people who haven’t voted Tory for years, or in the Leave case, a whole bunch of people who have never, ever voted because they felt their vote didn’t matter," Stephenson said.

“That’s why the key message she’s taken away is one of the need to control immigration and, particularly, the need to focus on the people who are struggling to get by.”

Gill added that industry needed to grasp the political reality in order to prepare for the blizzard of regulatory change on the horizon.

“The point that we are trying to make to businesses is that now we are leaving the EU, there’s going to be a whole host of laws — 20,000 in fact — that will come under the jurisdiction of the U.K. parliament," he said.