Many people voted for Brexit because they were fooled into a fear of “80m Turks coming to live in their village”, Vince Cable has said.

The likely next Liberal Democrat leader pointed to the notorious claim by the Leave campaign that Turkey was poised to join the EU as a key reason for the result.

The comment came as Dr Cable claimed the prospect of Brexit being aborted was “now becoming very real”, as politicians and civil servants confronted the daunting challenge.

The former Business Secretary also suggested Theresa May’s plea for Labour to work with her was an attempt to sign up Jeremy Corbyn to “force through a hard Brexit”.

And he said school funding — an issue where Theresa May is under pressure from within her own party — was an area where the Lib Dems would be willing to work with Conservatives.

During the Brexit campaign, Vote Leave released a video of David Cameron advocating Turkish membership of the EU mixed with scenes of brawling in the Ankara parliament.

Michael Gove was accused of Ukip-style rhetoric when he warned that Turkey and four other countries could join the EU as soon as 2020, leading to an influx of many millions of people.

Speaking to journalists at Westminster, Dr Cable pointed to that claim being raised in “church hall” meetings as an explanation for the referendum result.

“They were overwhelmingly elderly people who were obsessed by the worry of 80m Turks coming to live in their village,” he said.

“Immigration was a massive issue for them, although they had never actually encountered any [immigrants].

“In that age group — which was a very powerful one, mostly Conservative voting — there was a sense of nostalgia.

“The Britain they had been brought up in and loved, and felt comfortable with, was no longer there. And that was why they voted the way they did.”

Dr Cable confirmed the Lib Dems under his leadership would continue to campaign for a further referendum on any Brexit deal, insisting “people have the right to change their minds”.

He told The Independent he did not know the “pathway” to that vote taking place, but argued support would grow as the economic damage from Brexit began to bite.

“A lot of people who supported it are now worried about the consequences and we have got to provide some mechanism by which people can have that choice,” Dr Cable said.

He was “not a great fan of referendums”, but “the only way it can be ultimately closed as an issue is through another referendum”.

However, Dr Cable said he accepted a second referendum could deliver the same result. “That would kill the issue forever,” he admitted.

The 74-year-old is almost certain to be crowned as the new leader next week, without a fight, as the only candidate standing to replace Tim Farron.