More than 600 Members of Parliament politicians returned to the constituencies across Britain Thursday as Brexit was put on hold.

They started their Easter recess with a message from British Prime Minister Theresa May to return to Westminster on April 23.

Addressing MPs, May told them: "Let us use the opportunity of the recess to reflect on the decisions that will have to be made swiftly on our return after Easter. And let us then resolve to find a way through this impasse so that we can leave the European Union with a deal as soon as possible."

It may be a case of politicians being "de-mob" happy or just political fatigue, but many have admitted to feeling the strains of long, late night sittings and intensive debates about Britain's long-drawn out withdrawal from the EU.

Some MPs have even resorted to counselling to help them through the political maze created by Brexit.

May has won a delay from the EU which means politicians now have until October 31 to reach a withdrawal deal with Brussels.

But the prime minister remains committed to ending Britain's membership of the bloc long before then.

As MPs were packing their bags to head to train stations and airports for the journeys to their homes, stay-behind teams from May's Conservative government and the main opposition Labour Party were locked in their fourth round of private talks.

May and Labour leader Jeremy Corbyn are trying to find a way out of what has become an impasse in the search for an elusive Brexit deal.

Following the latest talks late Thursday between their two teams, May and Corbyn held a short meeting.

A spokesperson for the Labour leader said later: "Both sides agreed to continue talks in an effort to make substantive progress towards finding a compromise plan."

So far there are no clear signs that a breakthrough is close.

May's official spokesperson refused to say at a media briefing Thursday whether the prime minister plans to resign if she cannot get a deal through past MPs.

May had indicated, when her deadline was a June 30 departure date, that she would quit 10 Downing Street if a deal was agreed by the British parliament.

After agreeing to the extended deadline until October, May has faced renewed calls to quit from Conservative politicians angered by the delay to Britain's departure.

There were gasps in the chamber of the House of Commons when veteran Conservative MP Bill Cash asked May whether she was going to resign.

May responded: "I think he knows the answer", taken by politicians as a No.

Unless the parliament agrees on a withdrawal before May 22, Britain will have to take part in elections for British members of the European Parliament, at a cost of tens of millions of dollars.

The elected MEPs (Members of the European Parliament) would only serve until Britain ended its membership.

Conservative party managers across the country have said there is little mood for party workers to campaign for candidates, particularly as weeks earlier they will have been campaigning for council candidates in town and city local elections.

And although the front pages of Britain's national newspaper are likely to be virtual Brexit free zones for the coming days, the future of Britain's destination, in or out of the EU, will not be off the agenda for long.