LONDON — Under normal circumstances, the British lawmakers Nick Boles and Yvette Cooper would hardly be called rebels.

Mr. Boles, an Oxford-educated Tory, comes from a long line of colonial officers and Conservative Party stalwarts. Ms. Cooper, an Oxford-educated Labour lawmaker, became a government minister at the age of 30, and was the first woman to serve as chief secretary to the Treasury.

But on Tuesday, these two moderate, establishment lawmakers, both representing districts that strongly backed Britain’s exit from the European Union, hope to present the British government with a historic challenge.

They plan to propose an amendment in Parliament that could delay Britain’s departure from the bloc for a few months or even until the end of the year rather than leave without a deal.