A People’s Vote on Brexit could be organised quickly, Sir Vince Cable has insisted, despite the claims of the pro-Brexit “obstructionists,” and include the franchise being extended to 16-year-olds and ex-patriates.

The Liberal leader made his comments after the party’s high command took heart from London Mayor Sadiq Khan’s conversion to backing a second referendum on the final deal, which would include the option of Britain staying in the EU.

Jo Swinson, the Lib Dem’s deputy leader, said Mr Khan’s support, showed that “momentum is building to have a People's Vote on the deal".

Her colleague, Willie Rennie, who leads the Scottish Lib Dems, said the London Mayor had recognised that every day the promises made by the Leave campaign looked less and less believable.

“What’s more he’s speaking for the overwhelming majority of Labour members and Labour voters who don’t want to see Britain leave the EU,” insisted the Fife MSP.

He added: “Richard Leonard and Jeremy Corbyn need to recognise that the tide has turned. If they’re serious about protecting public services and our NHS, it’s time for them to speak out too.”

Later during a Question and Answer session with delegates, Sir Vince was asked what the timetable would be for a People’s Vote.

He replied: “There is a timetabling issue but it is not as formidable as the obstructionists claim. Let’s remember the world’s largest bank[Royal Bank of Scotland] was nationalised in a few weeks…”

He went on: “When people say now this is going to take months and months to get through Parliament, they are misleading you; it could be done very quickly.”

To applause, he added: “We do need to think about the modalities of a referendum. It’s not just a question of having a vote. We will want to ensure 16 and 17-year-olds have a vote. We want to ensure ex-patriates, who were deprived of their vote last time, have one.”

Writing in the Observer, Mr Khan warned the UK faced either a bad deal or no-deal, saying: "They are both incredibly risky and I don't believe Theresa May has the mandate to gamble so flagrantly with the British economy and people's livelihoods.”

Calling for another referendum, the London Mayor added: "This means a public vote on any Brexit deal obtained by the Government or a vote on a no-deal Brexit if one is not secured, alongside the option of staying in the EU.”

However, Barry Gardiner, the Shadow International Trade Secretary, who has previously argued against a People’s Vote, warning it could lead to civil disobedience, again exposed a major division on the issue within the party, saying a second poll would offer Theresa May a “lifeline because then she can say: 'Oh, if I can't get it through Parliament, I'll go back to the people'".

Meanwhile, the Tories launched a double attack on the People’s Vote.

Michael Gove, the Environment Secretary, dismissed Mr Khan’s call for a second referendum out of hand, saying he “wants essentially to frustrate the vote we had two and a half years ago. People voted clearly, 17.4 million people voted to leave the EU, and Sadiq is essentially saying: ‘Stop, let’s delay that whole process and throw it into chaos.’ That would be a profound mistake”.

His Tory colleague Brandon Lewis, the Conservative Chairman, said it was now clear Labour wanted to “keep the UK in the EU beyond March 2019; almost three years after the country voted to leave”.