LONDON — As a law to prevent a no-deal Brexit hurtled toward passage on Thursday, British lawmakers began drawing the battle lines for their next fight: when to hold a general election that is now inevitable.

Opposition lawmakers have so far blocked Prime Minister Boris Johnson’s plan for a mid-October election, but the government said on Thursday that it would hold another parliamentary vote on an early election on Monday.

That set up a significant clash over when British voters will get to decide who should handle Britain’s departure from the European Union, with opposition Labour lawmakers haggling over what stage of the Brexit process gives them the best chance of wrenching control from Mr. Johnson’s enfeebled government.

Mr. Johnson sees an election as the only way to create a stable majority for his Conservative Party in Parliament and secure a mandate for pulling Britain out of the European Union by Oct. 31, with or without a deal governing future relations.