LONDON • British Prime Minister Theresa May and her arch political rival Jeremy Corbyn are both signalling that they may be edging closer to a Brexit deal, after a month of talks between their teams that seemed to be going nowhere.

Both the government and the main opposition Labour Party talked up the prospects for a compromise plan and will hold more negotiations in the days ahead. The Prime Minister is aiming to wrap up the talks next week, either with an agreement or without one.

Mrs May signalled on Wednesday she could move on one of her key red lines and allow Britain to sign up to some kind of permanent Customs union with the European Union. The pound strengthened.

"There is a greater commonality in terms of some of the benefits of a Customs union that we've already identified between ourselves and the official opposition," she told a parliamentary committee. "Looking at the balance of these issues is part of the discussion. Can we come to an agreement on that? I hope we will be able to."

Mrs May invited Mr Corbyn to work on a cross-party deal last month in a desperate attempt to get an agreement, after the blueprint she negotiated with the EU was rejected for a third time by Parliament.

With local elections slated to take place yesterday, the talks have been low-key this week, but the government is planning one more big meeting next Monday or Tuesday to decide whether a consensus with Labour is possible.

For Mrs May, the key to any compromise on a Customs union is likely to be whether both sides can agree to call it something else.

That is because she has promised to take Britain out of the EU's Customs union, and pro-Brexit members of her Conservative Party would regard reversing this pledge as a major betrayal.

Meanwhile, Mr Corbyn's office gave Mrs May fresh hope. A Labour spokesman said what a Customs union is called is not the most important thing. Mr Barry Gardiner said in an interview on ITV's Peston show that "going for the compromise and seeing Jeremy Corbyn and Theresa May in negotiations, trying to work this through, is a sensible place for British politicians to be".

One of Labour's key demands in talks with the government is maintaining a joint Customs regime with the EU after Brexit so that businesses can continue to have tariff-free trade with the bloc.

Another point on which Mrs May and Mr Corbyn have some agreement is the question of a second referendum.

Mr Corbyn is resisting demands from within the Labour Party to make a referendum on the terms of a deal the price for supporting a joint plan with Mrs May.

Similarly, allies of the Premier say she is fiercely opposed to putting the question of Brexit back to voters, and would find it easier to support a Customs union.

Both government and Labour officials believe Mr Corbyn must now weigh up whether it is in his interests to help complete the EU divorce process.

His goal is to trigger a general election and replace Mrs May's Conservative Party in government. She has said she will stand down and make way for a new Tory leader once the Brexit divorce is done, and her successor could seek his own mandate in an election.

Mr Corbyn will also have an eye on the potential electoral threat from Mr Nigel Farage, whose new Brexit Party is aiming to eat into votes from Leave supporters in Labour constituencies.

The danger Mr Farage poses will be clearer if Mr Corbyn refuses to do a deal with Mrs May, and European Parliament elections are allowed to go ahead later this month.

BLOOMBERG