Theresa May received a Brussels kiss-off after her bid to break the Brexit deadlock was rejected as offering “nothing substantially new”.

But diplomatic sources revealed the Prime Minister did tell her fellow EU leaders that Britain was “ready to consider” extending the 21-month transition period by a year to December 2021 to give more time to seal a trade deal with the European bloc and eliminate the need for an Irish backstop.

Any such move would enrage Tory Brexiteers. One MP said: “It won’t fly.”

Mrs May had been asked to come up with new “concrete proposals” to unblock the impasse on the backstop issue but while she received a polite reception for her 30-minute presentation to fellow EU leaders, it appeared to have left them cold.

Antonio Tajani, the European Parliament President, said: “I listened carefully to what May had to say. The message was more relaxed than in Salzburg, certainly...but I did not perceive anything substantially new in terms of content.”

He explained how Mrs May had repeated her insistence that she would not assent to anything that would leave Northern Ireland in the EU's customs jurisdiction without the rest of the UK.

The SNP’s Stephen Gethins said it was clear the PM had “failed to bring forward any meaningful proposals to end the deadlock created by her Government”.

The party’s Europe spokesman added: “Rather than attempting to fudge her way through the negotiations, the PM should be using these meetings to constructively engage with our EU neighbours and to bring forward serious plans.”

Earlier, the PM insisted “now is the time” to agree a Brexit deal as she urged EU27 leaders to compromise on the Irish backstop to enable her to get a final agreement through Westminster by Christmas.

But Michel Barnier, the EU’s chief negotiator, made clear that a Brexit breakthrough would not happen any time soon and pointed to his earlier suggestion of extending the transition period by a year to December 2021.

He said: “We are not there yet. Brexit must be orderly for everyone and for all the issues, including on the island of Ireland. We need time, we need much more time…”

Mr Tajani also mentioned how Mrs May had shown a willingness to look into the possibility of extending the transition period following Brexit.

"Both sides mentioned the idea of an extension of the transition period as one possibility which is on the table and would have to be looked into," he explained.

However, any extension would rile the likes of Boris Johnson and Jacob Rees-Mogg as it would mean the continuation of free movement and Britain paying billions more pounds into EU coffers as the UK effectively remained in the European single market and customs union.

Nigel Farage, the former Ukip leader, said: "Mrs May's acceptance of an extension to the transition period will take us to the next General Election which may mean we never leave at all."

An extension would also mean the UK would not take back control of its waters until December 2021 at the earliest; more than five years after the EU referendum vote.

Bertie Armstrong of the Scottish Fishermen’s Federation said: “The EU must not be permitted to misuse the time when the UK is in the Brexit waiting room to try to place conditions on the return of fish stocks that are rightfully ours. That would backfire spectacularly.”

Today, Mrs May will have further bilateral meetings, having had talks on Wednesday with Jean-Claude Juncker, the European Commission President, Donald Tusk, the European Council President, Leo Varadkar, the Irish Taoiseach, and Emmanuel Macron, the French President.

As she arrived in Brussels, she sought to give an upbeat assessment of the talks, saying “very good progress” had been made since Salzburg both on the withdrawal agreement and the future partnership framework.

“Everybody around the table wants to get a deal. By working intensively and closely, we can achieve that deal. I believe a deal is achievable and now is the time to make it happen," declared the PM.

But Dalia Grybauskaite, the Lithuanian President, made clear there would be “no breakthrough” at the summit and said it was up to the UK to decide what it wanted and rally behind Mrs May.

"Today we do not know what they want. They do not know themselves what they want. It is a problem," she declared.

Asked if she was worried, Ms Grybauskaite replied: "Not yet. There is still time for the drama to play."

More voices have pointed to December as a deadline for a Brexit deal; a European Council is planned for the 13 and 14. Westminster rises on December 20 for Christmas. Any meaningful vote for MPs must have passed by then for the process of ratification by European parliaments to have any chance of being completed by Brexit Day on March 29 2019.

In a separate development, it became clear France and Germany were now drawing up contingency plans for Britain crashing out of the EU. Paris suggested Britons would need visas to travel to France in the event of a no-deal.

Meanwhile, a new row erupted at Westminster after the Government was accused of trying to prevent MPs having a meaningful vote on the final Brexit deal.

It emerged Dominic Raab had written to MPs, warning them that any Commons debates and votes should not “undermine” the final piece of Brexit legislation that implemented the deal.

The Brexit Secretary told the Commons Procedure Committee in a letter: “Once the deal is presented to Parliament, the procedure through which it is voted upon must allow for an unequivocal decision and one which is clear to the British public.”

Last night, it was suggested amendments would only be taken if the main Brexit motion was passed. If it was not passed, any amendments would be regarded as merely “points of view”.

Mr Raab noted: “Anything other than a straightforward approval of the deal will bring with it huge uncertainty for business, consumers and citizens.”

But Labour’s Sir Keir Starmer said his party did not accept the choice facing Parliament was between “whatever deal Theresa May cobbles together or no-deal”.

The Shadow Brexit Secretary said: “That is not a meaningful vote and ministers can’t be allowed to silence Parliament. MPs must be given the opportunity to scrutinise, consider and, where appropriate, amend any resolution the Government puts forward.”

A Labour colleague added: “This skulduggery must be resisted by all those MPs - whatever their view on Brexit - who truly believe in parliamentary sovereignty and taking back control. The Government is trying to stop Parliament having its say.”

Earlier in the Commons, Mrs May faced a raucous Prime Minister’s Questions. She insisted her Chequers Plan was “not dead” and made clear her ultimate red line was the protection of the "precious Union of the United Kingdom".

Jeremy Corbyn for Labour claimed Mrs May and her Government were “too weak and too divided to protect people's jobs, our economy or ensure there is no hard border in Northern Ireland".

At Scottish Questions, David Mundell vowed to defend Scotland's place in the Union "until my last breath".

The Scottish Secretary, who has made clear that any post-Brexit border down the Irish Sea would be a resignation matter for him, told MPs: "I make no apology for making absolutely clear that the integrity of the UK is a red line for me and my Scottish Conservative colleagues in any deal on leaving the EU. The position is exactly the same for our Prime Minister.”