LONDON — Gina Miller says she receives online death threats most days, thanks to her recent legal case that forced Britain’s government to consult lawmakers over its plans to leave the European Union.

But Ms. Miller, an investment fund manager and the lead claimant in the successful case centering on the procedure for invoking Article 50, the legal mechanism for leaving the bloc, has entered another fight that could bring her more recrimination.

This time, she is leading a tactical voting campaign called Best for Britain, which aims to help pro-European candidates in the general election here on June 8 in the hope that their influence can soften the impact of “Brexit,” as the country’s withdrawal from the bloc is known.

The group wants to restrict the scale of Prime Minister Theresa May’s probable victory — Mrs. May has said she wants to secure a large parliamentary majority in order to strengthen her hand as she negotiates Britain’s divorce. The Best for Britain campaign hopes to weaken her hand and prevent a so-called hard Brexit, or clean break from the bloc, if that is the strategy Mrs. May pursues. She has, for instance, ruled out retaining membership in the European Union’s single market.