THERESA May has said she is hopeful of a "swift" move to talks on Britain's future trade relationship with the EU following the two-day summit in Brussels.

Today, leaders of the remaining 27 EU nations are expected to give their approval to a draft agreement on the terms of the UK's withdrawal from the EU, including a post-Brexit transition period lasting until the end of 2020.

Donal Tusk, the European Council President, has recommended endorsement of the deal, which he said would put off "the negative consequences of Brexit" for another 21 months after the formal date for the UK's withdrawal in March 2019.

At the summit, the Prime Minister said: "We made considerable progress through the agreement on the implementation period, which will bring certainty to businesses and people.

"I look forward to the European Council endorsing that agreement and moving on swiftly to talk about the future partnership that we all want to build together."

Under the terms of the joint legal text agreed by Brexit Secretary David Davis and the EU's chief negotiator Michel Barnier the UK will be able to negotiate and ratify trade deals with outside countries during the transition period, to come into effect on January 1 2021.

On Wednesday, Mrs May told MPs that for the first time in 40 years Britain would be able to "forge our own way by negotiating our own trade agreements".

However, the PM faces warnings that the deal could be scuppered by her own MPs unless she tears up "unacceptable" proposals for fishing.

Some 14 of the PM's backbench parliamentary allies - 13 Conservatives and one DUP MP - have signed a joint letter denouncing the draft deal agreed by the Government earlier this week.

In Brussels, Mrs May met Irish Taoiseach Leo Varadkar for one-on-one talks on the margin of the summit and was also due to have a meeting with German Chancellor Angela Merkel and French President Emmanuel Macron.

Mr Varadkar made clear that an Irish border deal had to be completed by October otherwise a “backstop” option would mean Northern Ireland continuing to follow EU regulations after Brexit; effectively, staying in the customs union, which is anathema to Mrs May.

He said: "Everyone takes the view that we will have to have the withdrawal treaty agreed by October because it will have to be ratified by the British Parliament and the European Parliament, and potentially by some national parliaments. So October is the deadline.”

The Taoiseach said he envisaged a really close trading relationship between the UK and the EU, adding: “So close that many of measures in the backstop may become unnecessary."

But Stephen Donnelly, Fianna Fail’s Brexit spokesman, warned Ireland's leverage on the border issue was rapidly declining the further the talks continued between the EU and Britain.

"As the talks progress, many other important issues for other EU member states will come to the fore with the border becoming one of many competing priorities," he said.