The communications director for Vote Leave has said there should be a referendum on Theresa May’s Brexit deal if people “don’t like it”.

Paul Stephenson played a leading role in the official leave campaign led by Michael Gove and Boris Johnson.

“I’m a democrat. Of course if we get a deal and people don’t like it, there should be another vote,” he told a technology conference in Lisbon on Tuesday.

Stephenson told HuffPost UK while he had not “defected” to the People’s Vote campaign – if there was a “groundswell of opinion” for a referendum on the final deal he would not be against it.

“I believe in referendums on major constitutional issues,” he said.

May has repeatedly ruled out holding another referendum. But campaigners hope when the prime minister’s deal is put to a vote in Parliament a way can be found to force another public vote.

May is facing demands from both her own Cabinet that she show them the legal advice behind her Brexit plan.

Cabinet ministers were invited this afternoon to read the elements of the draft withdrawal agreement that have been agreed with Brussels.

Amanda Chetwynd-Cowieson, from the pro-EU For our Future’s Sake campaign, welcomed the unexpected intervention from Stephenson. “See you on the campaign trail, Paul,” she said.

Campaigners pushing for a so-called People’s Vote have also seized on past suggestions from senior Brexiteers including Jacob Rees-Mogg, David Davis and John Redwood that two referendums would be needed.

Dominic Cummings, the campaign director of Vote Leave, previously suggested people be given a second vote.

“As a matter of democratic accountability, given the enormous importance of so many issues that would be decided in an Article 50 renegotiation – a far, far bigger deal than a normal election – it seems right to give people a vote on it,” he wrote in 2015.

“As it happens, it might make more sense to have the second referendum after the renegotiation is completed,” Rees-Mogg told the Commons in 2011.

Speculation that a Brexit deal is close was fuelled by documents leaked to HuffPost UK and others apparently setting out how the prime minister would sell an exit package to the public.

Downing Street distanced itself from the blueprint, but the document heightened suspicion among Tory Brexiteers that a deal has secretly been secured.

Number 10 said the “childish language” and misspelling in the notes, which includes the incorrect spelling of the Irish prime minister’s name, should make it clear it “doesn’t represent the government’s thinking”.