British Prime Minister Theresa May says her Conservative government and the opposition Labour Party have a duty to strike a compromise Brexit agreement to end months of political deadlock over Britain's exit from the European Union.

Writing in the Mail on Sunday, May told Labour leader Jeremy Corbyn: "Let's do a deal."

She said a cross-party compromise was not her first choice, but "we have to find a way to break the deadlock."

The Conservatives are desperate to move forward after losing hundreds of positions in last week's local elections. Labour also suffered losses as voters punished both main parties for the Brexit impasse.

But the prospect of the government compromising and accepting Labour's demand for close economic ties with the EU has infuriated pro-Brexit Conservatives, who are demanding May's resignation.