Theresa May will make the improved offer when she next meets Jean-Claude Juncker YVES HERMAN/REUTERS

Britain will pay EU bills for decades after the government bowed to demands from Brussels to meet its long-term financial liabilities to the bloc.

Theresa May will make an improved offer next week in which she will promise to pay the costs of all existing EU projects and pensions signed off while Britain was a member.

The cost, likely to be between €40 billion and €50 billion in total, will not be settled as a lump sum but will be spread over a period of up to 40 years on a diminishing scale “when they [the bills] fall due”.

EU diplomats expect the prime minister to use that language when she tables the offer at a meeting on Monday with Jean-Claude Juncker, president of the…