Theresa May is welcomed by European Commission president Jean-Claude Juncker prior to a meeting in Brussels

Donald Trump has said Theresa May's Brexit agreement "sounds like a great deal" for the EU, and may hinder trade between the UK and US.

The US president issued his warning hours after the prime minister faced an onslaught of criticism from hostile MPs in the Commons as she pitched her Brexit deal to them, saying that rejecting the agreement would cause division and uncertainty.

The date of the MPs’ vote on the agreement was revealed as 11 December, giving the prime minister a fortnight to avert what threatens to be a humiliating defeat at the hands of scores of Conservative rebels.

In a debate lasting nearly three hours, Ms May was forced time after time to defend her strategy as Tory grandees and opposition members alike lined up to attack aspects of the withdrawal agreement signed in Brussels at the weekend.

She was loudly barracked by MPs as she insisted that no better deal was available than the agreement and political declaration on future relations endorsed by EU leaders.

Former minister Mark Francois branded her deal a “surrender”, saying opposition from Eurosceptic Tories and the Democratic Unionist Party meant it was already “dead as a dodo”.

Former defence secretary Sir Michael Fallon described the deal as “a huge gamble” that involved the UK paying a £39 billion divorce bill and giving up its votes and veto without any firm commitment on future trade relations.

But Mrs May said: “The British people want us to get on with a deal that honours the referendum and allows us to come together again as a country, whichever way we voted.

“This is that deal. A deal that delivers for the British people.”

In a sign that she aims to go over fractious MPs’ heads and appeal directly to voters for their backing, Ms May said parliamentarians had a “duty” to listen to their constituents before taking their decision in the national interest.

But Labour leader Jeremy Corbyn said the Commons would have “very little choice” but to reject the “botched” deal, which he described as “bad for this country”.

With 90 or more Conservative MPs indicating they could rebel in the “meaningful vote”, Brexit Secretary Stephen Barclay admitted the prime minister faces a “challenging” division.

No one knows what would happen if this deal doesn’t pass Theresa May

European Commission president Jean-Claude Juncker warned that there would be no more negotiation if MPs vote down the agreement, saying: “This is the best deal for Britain ... and this is the only deal possible, so if the House says no, we would have no deal.”

Ms May told MPs: “I can say to the House with absolute certainty that there is not a better deal available.”

She said MPs faced a choice: “We can back this deal, deliver on the vote of the referendum and move on to building a brighter future of opportunity and prosperity for all our people.

“Or this House can choose to reject this deal and go back to square one.

“Because no one knows what would happen if this deal doesn’t pass. It would open the door to more division and more uncertainty, with all the risks that will entail.”

Mr Corbyn said: “The prime minister says if we reject this deal, it will take us back to square one. The truth is, under this government we have never got off square one.

“This botched deal is still a bad deal for the country and all yesterday did was mark the end of this government’s failed and miserable negotiations.”

Ms May told MPs the government had ensured that Gibraltar was covered by the withdrawal agreement and would negotiate a future relationship “for the whole UK family, including Gibraltar”.

A two-hour Cabinet meeting earlier heard an update from Mr Barclay on preparations for a possible no-deal Brexit, which are continuing despite the deal being agreed.

After the Commons debate, Downing Street chief of staff Gavin Barwell and effective deputy prime minister David Lidington invited opposition MPs to a briefing on the agreement.

But Downing Street sources said they were not aware of the prime minister seeking to speak to Labour MPs thought to be considering backing her deal.

Analysis by the Bank of England and the Financial Conduct Authority of the impact of the deal on the UK economy is to be published on Thursday.

Ms May has started a campaign to sell her deal directly to the public, with visits to all parts of the UK planned.

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Her spokesman declined to confirm or deny reports that No 10 is considering a possible television debate with Mr Corbyn, something the Labour leader has made clear he would relish.