LONDON — Prime Minister Theresa May of Britain was battling to save her government on Monday after her foreign secretary quit in protest over her approach to withdrawing from the European Union. The resignation deepened a mood of crisis just eight months before the country is due to leave the bloc.

The foreign secretary, Boris Johnson, was the second minister to leave Mrs. May’s cabinet within 24 hours. He stepped down after she pushed ahead with a proposal that would keep Britain more closely tied to the European Union than hard-line conservatives want.

“We are truly headed for the status of colony,” Mr. Johnson said in his resignation letter.

It has been two years since Britons voted to leave the European Union in a referendum that rattled governments on the Continent and beyond. But actually severing the intricate economic ties that bind Britain to the rest of Europe has proved far more complicated than merely casting a ballot at the polls.

Many Britons remain opposed to leaving the bloc, and even among those who favor it, there are deep divisions. Some, like Mr. Johnson, advocate a clean break — or, at least, taking that stance in withdrawal negotiations with the European Union. Others, like Mrs. May, support maintaining at least some ties, including abiding by some European regulations.