British Prime Minister Theresa May has said that progress had been made in solving the impasse over the backstop arrangements for the Irish border, but added that time was running out to secure changes.

Speaking following a meeting with European Commission President Jean-Claude Juncker in Brussels, Mrs May said that time "is of the essence".

"I've underlined the need for us to see legally binding changes to the backstop that ensure that it cannot be indefinite. That's what is required ... We've agreed that work to find a solution will continue at pace," she said.

"Time is of the essence, and it's in both our interests that when the UK leaves the EU, that it does so in an orderly way. So we've made progress."

The backstop provides for Britain to remain in the EU customs union until a way is found - such as a future free trade deal - to ensure that Ireland's border with Northern Ireland remains open.

Brexiteers in Mrs May's Conservative party see this as a "trap" to keep Britain in a form of union indefinitely, and have demanded a time limit or a unilateral exit clause.

In a joint statement following the meeting, Mr Juncker and Mrs May said that they will speak again before the end of the month.  

Earlier today, Mrs May said she would bring a vote on a revised Brexit deal back to parliament as soon as possible.

However, she said that she would do so only when it was the right time after securing changes to it from the European Union.

"Obviously we are in these discussions with the European Union and we will bring a vote back to this house when it is possible to bring a deal that deals with the issue that the House of Commons has raised," she told parliament.

"We have listened to the House of Commons, we are working on the views of the House of Commons with the European Union, and we will bring a vote back when it is the right time to do so."

With less than six weeks until Brexit day, EU leaders have insisted they will not restart negotiations.

Today, three MPs quit the Conservative Party to join a new Independent Group. The MPs hit out at Mrs May's "disasterous" handling of Brexit.

Earlier, she issued a plea to Conservative MPs to unite and deliver on Brexit, urging her party to "move beyond what divides us" and sacrifice "personal preferences".

Mrs May, in a letter to all her Conservative MPs after her Brexit plans suffered another humiliating Commons defeat on 14 February, said the result was "disappointing" but vowed that the government would continue its work to secure changes to the Irish border backstop.

Mrs May and the other 27 EU leaders approved a Brexit withdrawal agreement at a summit on 25 November, but the parliament rejected it on 15 January.

Since then, Mrs May and her ministers have repeatedly met EU leaders and their negotiator Michel Barnier to urge them to reopen the text to find a way to appease eurosceptic MPs.

Without a deal, Britain is due to leave the EU abruptly after four decades on 29 March, with no follow-on agreement or transition period to manage trade and economic relations.

Both sides have said they want to avoid this, and many experts foresee economic chaos, even warning of food and medicine shortages or a renewed threat of unrest in Northern Ireland.

Manufacturing supply chains could be disrupted, and Brexit uncertainty has already been cited as a contributing factor in the closure or departure of several British-based businesses.

Another option would be for Brussels to accord Britain an extension to the 29 March deadline, which is enshrined in British law.

But Mrs May's government insists it will not request a delay, all 27 remaining members would have to agree and it would be legally difficult for Britain to remain in the EU for long.