The Conservatives and Labour could both break apart in the coming months because of internal divisions over Brexit, Vince Cable has said.

The Liberal Democrat leader said that for the first time in his lifetime he believed there was a real prospect of splits because Tory moderates are “in a terrible state” and “hardliners” have “complete control” of Labour.

He was speaking at an IndyMinds event in central London for subscribers of The Independent.

Asked about the prospect of a possible split in the main parties, he said: “I think for the first time in my lifetime this is possible.

“In the last few days I’ve been having conversations with deep-dyed Tories – the kind of people you would never regard as wet or one-nation Tories.

Opposing protesters flock to parliament on would be date of Brexit Show all 30 1 /30 Opposing protesters flock to parliament on would be date of Brexit Opposing protesters flock to parliament on would be date of Brexit Pro-Brexit leave the European Union supporters attend a rally in Parliament Square after the final leg of the "March to Leave" in London AP Opposing protesters flock to parliament on would be date of Brexit The protest march which started on March 16 in Sunderland, north east England, finished on what was the original date for Brexit to happen before the recent extension Reuters Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter holds up a poster during a rally after the final leg of the "March to Leave" in London, Friday, March 29, 2019. Pro-Brexit demonstrators were gathering in central London on the day that Britain was originally scheduled to leave the European Union. (AP Photo/ Kirsty Wigglesworth) Kirsty Wigglesworth AP Opposing protesters flock to parliament on would be date of Brexit A pro-Brexit protester holds a sign next to a statue of Winston Churchill at the March to Leave demonstration in London, Britain March 29, 2019. REUTERS/Toby Melville TOBY MELVILLE Reuters Opposing protesters flock to parliament on would be date of Brexit Brexit demonstrators in Parliament Square in Westminster, London. PRESS ASSOCIATION Photo. Picture date: Friday March 29, 2019. See PA story POLITICS Brexit. Photo credit should read: Jonathan Brady/PA Wire Jonathan Brady PA Opposing protesters flock to parliament on would be date of Brexit Pro-Brexit protesters hold signs and wave flags at the March to Leave demonstration in London, Britain March 29, 2019. 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“They say, ‘We’ve just had it up to here – we just cannot take any more of it. Our party’s been infiltrated by the right-wing equivalent of Momentum, we’ve been threatened in our seats, we’ve had to get legal advice.' They’re in a terrible state these moderate Tories.

“And then on the Labour side you have one desperate effort being made by [deputy leader] Tom Watson, who is a very formidable and impressive guy, to try and save the Labour Party, but even those who like him and hope for the best are pretty pessimistic because the hardliners have complete control.

“You may well find that if this crisis continues for much longer then both of the traditional parties do split, and that creates the perfect condition for something new and better.”

Sir Vince said he wanted his party to work closely with The Independent Group, which is registering as a political party called Change UK - saying it would be “foolish and shortsighted” for the two parties to field candidates against each other.

He said: “As long as I’m leader I’m keen to bring us together. There are tribal people in any organisation who won’t work like that, but I’m personally determined that as long as I’m around, we do our best to bring people together.”

He added: “We can’t compete with them or them with us because it will destroy us both. It would be an absurd thing to do because we’d simply be splitting the centrist vote under a first-past-the-post system, so they are going to have to collaborate with us.”

He was speaking hours after MPs rejected Theresa May’s Brexit deal for a third time.

Speaking immediately after the vote, Ms May told MPs it was likely that the UK would now have to seek a long delay to Brexit and hold European Parliament elections in May.

She said: “The implications of the House’s decision are grave.

“The legal default now is that the United Kingdom is due to leave the European Union on 12 April – in just 14 days’ time.

“This is not enough time to agree, legislate for and ratify a deal, and yet the House has been clear it will not permit leaving without a deal, and so we will have to agree an alternative way forward.”

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The prime minister also hinted at the prospect of a general election, warning MPs: “I fear we are reaching the limits of this process in this House.