LONDON—More than two years after Britons voted to leave the European Union, the U.K.’s politicians still can’t agree on what kind of Brexit they want. Now more lawmakers are calling for a do-over, a second referendum that could potentially reverse the results of the first.

About 150 members of Parliament back a new vote, including Labour, Scottish nationalists and a handful of Conservative legislators, according to Dominic Grieve, a Conservative member of Parliament who is supporting a fresh vote.

That...