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Cross-party MPs in Parliament could block a no-deal Brexit, Labour’s John McDonnell has said.

The shadow chancellor appeared on the BBC’s Andrew Marr show and said he believes Theresa May lacks a majority in the House of Commons for a no-deal exit, adding he is "not willing to countenance" such an outcome.

He hinted that rebel Tory MPs are in talks with Labour to give Parliament the power to veto a no-deal Brexit, forcing the Government to "come to their senses and negotiate properly".

The European Union (Withdrawal) Bill is notably absent from the Commons schedule for the week ahead, with the Government saying it wants to closely evaluate some 300 amendments and more than 50 new clauses proposed.

Mr McDonnell told BBC One's Andrew Marr Show: "I don't think there's a majority for no deal. I think on a cross-party basis you'll see in the debates in the coming week - the Government will get the message, there will be a deal."

Asked if the Commons could stop the Government over no-deal, Mr McDonnell said: "I don't believe there's a majority in the House of Commons for a no deal and I think the Government needs to recognise that."

Speaking about giving Parliament the power to have a say over the final exit deal, the Labour frontbencher added: "When we amend the legislation, which I think we will, I think there's a majority to do that, to have a meaningful vote.

"That's what we've said all the way along. We'll be able to say to Government whatever you're negotiating, it'll not be on the basis of no deal because the damage to this economy will be so great."

Mr McDonnell claimed the Tories are "fighting among themselves" rather than negotiating with the EU.

When told Labour cannot stop this, Mr McDonnell replied: "Parliament can. They haven't got a majority to get through a no deal situation.

"If we amend the legislation for Parliament to have a meaningful vote, it'll force the Government to negotiate - come to their senses, negotiate properly."

Asked if this included talks with Tory MPs, Mr McDonnell replied: "There are discussions going right the way across the House."

Pressed when the vote will be, the Labour MP said: "Shall I tell you why we're not seeing a vote next week?

"Not because there's 300 amendments that have been put down - most of them actually their own side - but because they're now negotiating with their own backbenchers on just how much they can get through.

"They're more interested in negotiating to save the Conservative Party than they are in the interests of the country.

"That's why I think actually it's a disgrace. They should come to their senses, behave responsibly and look after the interests of the country."

Chris Grayling said Mr McDonnell was "talking a lot of complete nonsense" when he suggested there was enough support in the Commons to stop the Government taking the no deal route.

"Parliament has already voted to leave the European Union," the Tory MP told Marr.

"John McDonnell threatening to derail this bill is John McDonnell threatening to create the kind of chaotic Brexit he himself is warning against."

He insisted Britain will "succeed whatever happens" but said it would be bad for the EU if no agreement was struck.

The Government is planning for all eventualities, the Transport Secretary added.

Asked what would happen to food prices if there was no deal, he told Marr: "It would mean that producers, supermarkets bought more at home, that British farmers produced more, that they bought more from around the world and it would damage French producers and continental producers."

Mr Grayling said the negotiations were where he "expected them to be" and insisted no one had believed they would be done in "half an hour".

"This was always going to be a long and difficult negotiation," he said.

Mr Grayling was played a clip of a previous interview he gave in which he said he had "no doubt at all" the UK would continue to trade tariff-free with the EU.

"I still agree with myself," he told the programme.

Flights "will carry on" even if the negotiations fail, he said.

Despite weeks of Tory turmoil over Brexit, Mr Grayling insisted the Cabinet is united on wanting the best deal for Britain but said the Government must be "upbeat" about the future.

He dismissed suggestions Chancellor Philip Hammond was sabotaging Brexit.

Asked if he should be sacked, Mr Grayling said: "In a month's time the Chancellor is going to deliver a very important budget for this country and I'm working with him and we are all behind him in delivering that."

Additional reporting by Press Association.