Cross-party talks to resolve the Brexit crisis are reaching the end, Prime Minister Theresa May's government indicated Tuesday, with reports suggesting she wants a conclusion by the middle of next week.

Ministers held their latest talks on Monday with senior members of the main opposition Labour party.

They are seeking a way through the political deadlock over how to leave the European Union, which has forced Britain to twice delay its intended exit.

"There were serious and constructive discussions last night, and we will now look to hold further talks in the coming days," May's spokesman said.

"Further talks will now be scheduled in order to bring the process toward a conclusion," he added.

No announcements are expected this week due to local elections being held on Thursday, but the spokesman said progress must be made "as soon as possible".

Reports suggest the government is aiming to decide by the middle of next week if the talks will ever succeed, or if they should be abandoned.

May has said that if no deal is possible with Labour, she would ask MPs to vote on a series of possible options.

The House of Commons has three times rejected the divorce deal she struck with the EU in November, intended to ease Britain's split from its largest trading partner after four decades of membership.

But MPs have also been unable to agree on any alternative.

"There's a full understanding throughout cabinet and the government of the need to make progress," May's spokesman said, after a meeting of the cabinet.

The prime minister agreed with the EU earlier this month to delay Brexit until October 31 to find a way through the political impasse. It was originally scheduled for March 29.

However, May is still hopeful of getting her deal passed in the coming weeks to allow Britain to avoid holding European Parliament elections on May 23.

If that is not possible, she hopes to avoid any lawmakers elected in that poll having to take their seats.