THERESA May is to go back to the EU to try to renegotiate her Brexit deal after MPs gave their backing to proposals to replace the controversial backstop.

But she earned an immediate rebuff from Brussels, where European Council president Donald Tusk insisted that the Withdrawal Agreement struck last November was not open for renegotiation.

Meanwhile, one of Mrs May's strongest negotiating weapons was ripped from her hands by MPs who voted to block a no-deal Brexit.

In a night of high drama at Westminster, the Commons voted by 317 to 301 in favour of a proposal backed by the Prime Minister to reopen the Withdrawal Agreement and replace the backstop with "alternative arrangements" to avoid a hard border in Ireland.

Mrs May said that the result showed there was a means of securing a "substantial and sustainable majority in this House for leaving the EU with a deal" and vowed to seek a new agreement with Brussels.

But in a statement, Mr Tusk's spokesman said: "The Withdrawal Agreement is and remains the best and only way to ensure an orderly withdrawal of the UK from the European Union. The backstop is part of the Withdrawal Agreement, and the Withdrawal Agreement is not open for re-negotiation."

And French President Emmanuel Macron also said the agreement was "not renegotiable", in comments just moments before MPs voted.

The Commons approved a cross-party amendment, tabled by Midlands MPs Caroline Spelman and Jack Dromey, rejecting a no-deal Brexit by 318 to 310.

The vote is not legally binding on the Government but will impose massive political pressure on the Prime Minister to delay Brexit from its scheduled date of March 29 if she cannot secure a new deal from Brussels.

The PM told MPs: "I agree that we should not leave without a deal. However, simply opposing no-deal is not enough to stop it.

"The Government will now redouble its efforts to get a deal that this House can support."

There was uproar in the chamber as she said: "There is limited appetite for such a change in the EU and negotiating it will not be easy. But in contrast to a fortnight ago, this House has made it clear what it needs to approve a withdrawal agreement."

Mrs May said she would seek "legally binding changes to the Withdrawal Agreement that deal with concerns on the backstop while guaranteeing no return to a hard border".

And she told MPs: "If this House can come together, we can deliver the decision the British people took in June 2016, restore faith in our democracy and get on with building a country that works for everyone.

"As Prime Minister I will work with members across the House to do just that."

Tuesday's votes were triggered by the overwhelming defeat of Mrs May's Brexit Plan A by 230 votes earlier this month.

Labour leader Jeremy Corbyn, who boycotted cross-party talks after that vote, said that he was now ready to meet the Prime Minister to discuss a "sensible Brexit solution that works for the whole country".

Mr Corbyn said: "Tonight Parliament has voted to remove the immediate threat of crashing out without a deal on 29 March. After months of refusing to take the chaos of no-deal off the table, the Prime Minister must now face the reality that no-deal is not an option."

Scottish National Party Westminster leader Ian Blackford said the Conservatives had "effectively ripped apart the Good Friday Agreement".

But the Democratic Unionist Party's Nigel Dodds, whose party backed the amendment tabled by Tory grandee Sir Graham Brady, said it was "utterly reckless to talk in those terms".

Mr Dodds said: "This is a significant night because for the first time the House by majority has expressed what sort of deal will get through and will have a majority, and we will work with the Prime Minister to deliver the right deal for the United Kingdom."

In a dramatic series of votes, MPs rejected two proposals to delay Brexit by extending the two-year Article 50 negotiation process if Mrs May was unable to secure an acceptable agreement by February 26.

And they also voted down a plan by former attorney general Dominic Grieve for a sequence of "indicative votes" to establish MPs' preferred Brexit outcome.

The pound dipped sharply after the failure of the attempts to delay Brexit, losing around 0.7% against both the US dollar and euro, though there were indications later that it may be rising.

CBI director general Carolyn Fairbairn described it as "another deeply frustrating day for British business".

"The Brady amendment feels like a throw of the dice," she said.

"It won't be worth the paper it is written on if it cannot be negotiated with the EU. Any renegotiation must happen quickly - succeed or fail fast."

Former foreign secretary Boris Johnson dismissed Mr Tusk's statement, telling Sky News: "There is a negotiation going on. You would expect him to say that. But believe me the EU has every incentive to give us the deal we need."

But the Irish Government said in a statement: "The Withdrawal Agreement is not open for re-negotiation.

"The agreement is a carefully negotiated compromise, which balances the UK position on customs and the single market with avoiding a hard border and protecting the integrity of the EU customs union and single market.

"The best way to ensure an orderly withdrawal is to ratify this agreement."