The Liberal Democrats will fight the next general election with a pledge to take Britain back into the EU, claiming the referendum result was secured on a campaign of lies.

Voters backed Brexit in a “howl of anger” at out-of-touch politicians, but must be given the chance to rethink the decision, according to the Lib Dem leader, Tim Farron.

The cheap slogans of Ukip’s Nigel Farage and Tories Boris Johnson and Michael Gove are unravelling, and the public will feel betrayed when promises on the NHS and immigration are not delivered, the party said.

Since the shock referendum result, the Lib Dems have recorded thousands of voters signing up to become members.

Farron said he will make the case for the country to rejoin the EU at the next general election.“For many millions of people, this was not just a vote about Europe,” he said. “It was a howl of anger at politicians and institutions who they felt were out of touch and had let them down.

“The British people deserve the chance not to be stuck with the appalling consequences of a leave campaign that stoked that anger with the lies of Farage, Johnson and Gove.

“The Liberal Democrats will fight the next election on a clear and unequivocal promise to restore British prosperity and role in the world, with the United Kingdom in the European Union, not out.

“If you agree with us, join us to make this happen.”

The next general election is not due until 2020 under current laws, but could be staged within months if the next Conservative leader decides to seek a mandate through a national vote.

They would have to secure a two-thirds Commons majority, repeal legislation or see a vote of no confidence in the government for a snap poll to go ahead.

A Lib Dem spokesman said: “In 24 hours the cheap bus slogans of Farage, Johnson and Gove are unravelling.

“On £350m for the NHS, on immigration, it is clear that they will fail to deliver what people thought they had voted for. Once again, people will feel betrayed by out-of-touch politicians.

“The Liberal Democrats are the only party united behind a future for Britain inside the European Union.”