British Prime Minister Theresa May said she would seek a “pragmatic solution” to the impasse over Brexit when she tries to reopen talks with Brussels in the coming days.

Writing in The Sunday Telegraph newspaper, May said she would be “battling for Britain and Northern Ireland” when she returns to speak to EU politicians.

UK MPs last week backed a call for May to return to Brussels to secure a new Brexit deal that puts “alternative arrangements” in place of the controversial backstop — a kind of insurance policy designed to avoid a hard border between Northern Ireland and the Irish Republic.

Under the backstop, the UK would remain in a customs union with the EU in the absence of a trade deal, and Northern Ireland would stay aligned to some EU rules.

Critics say that an unlimited backstop would effectively give the EU a veto on future British trade arrangements with other countries, and weaken economic ties between Northern Ireland and the rest of the UK.

READ MORE: What ‘alternative arrangements’ are there to the Irish backstop?

May argued that lawmakers would be “happy with the current backstop if there was a time limit or unilateral exit mechanism.”

“I will be armed with a fresh mandate, new ideas and a renewed determination to agree a pragmatic solution that delivers the Brexit the British people voted for, while ensuring there is no hard border between Northern Ireland and the Republic of Ireland,” she wrote.

However, EU leaders have maintained that the Withdrawal Agreement, including the backstop, cannot be renegotiated.

Despite the challenges, May insisted in the article that she would “deliver Brexit on time”.

In an interview with Sky News, British trade minister Liam Fox said it would be "irresponsible" for the EU to refuse to reopen negotiations over the Brexit deal.

"Are they really saying that they would rather not negotiate and end up in a 'no-deal' position?" Fox told Sky News.

"It is in all our interests to get to that agreement and for the EU to say we are not going to even discuss it seems to me to be quite irresponsible."

Fox also suggested that delaying the exit date might be admissible if the UK just needed more time to get the necessary legislation in place for a smooth exit.

"There is a big difference between if we had an agreement and we need some time to get the legalities done, that is one thing," Fox said. "I think to extend simply because we hadn’t reached an agreement would not provide any impetus for that agreement to be reached."

The UK is due to leave the EU at 12pm CET on March 29.

Confused by Brexit jargon? We break it down for you here and in the video below.