STAMFORD, England — The Conservative lawmaker Nick Boles stood at the altar of a 15th-century church last week, gazing out at the people who held his political future in their hands.

They were lingering at the back of the church: a cluster of men and women in their 60s, mostly white-haired and wearing sensible coats. They were the leaders of the local conservative association, the ones deciding whether to expel Mr. Boles from his seat for trying to block a no-deal Brexit. Party leaders see the threat of no-deal as a key lever in last-minute negotiations with the European Union.

“He has let us down badly,” said Philip Sagar, chairman of the Grantham and Stamford Conservative Association. “I cannot vote for someone who is selfish,” said Matthew Lee, the leader of the District Council.

On Monday, the leaders of the local conservative association voted to start a protracted process that could result in deselection, which would prevent him from seeking re-election as a Tory. His fate is being watched closely as a bellwether of whether the Conservative Party will go on to purge other members who do not support the party’s Brexit strategy.