LONDON — After more than a year of drama, recrimination and tense, late-night votes, British lawmakers signed off Thursday, with minimal fuss and no fanfare, on legislation to take their country out of the European Union at the end of the month.

The vote in the House of Commons is not quite the final parliamentary moment of Britain’s Brexit story — the bill will be considered next by the unelected second chamber, the House of Lords — but the suspense that surrounded many previous votes was entirely absent.

Even if the Lords amend the bill, Prime Minister Boris Johnson and his Conservative Party now have a large majority in the Commons and could overturn any changes — swiftly, if necessary. The legislation is almost certain to be completed and written into law next week.

They approved the bill on a vote of 330-231, drawing a long-awaited line under the heated debate over a Brexit plan that convulsed British politics.

Once the exit plan has also been approved by the European Parliament, the stage will be set for Britain to reverse more than four decades of integration with its continental neighbors, a journey that began when it entered what was then called the European Economic Community in January 1973.

What comes next remains far from clear — the deal set to go into effect Jan. 31 establishes a transition period, and the two sides are preparing for negotiations on a long-term trade deal and on other future ties. Those talks are expected to revive many of the cross-Channel tensions in evidence since the 2016 referendum in which Britain voted to leave the European Union, convulsing the country’s politics.

Big constitutional questions remain, and Wednesday the Scottish Parliament refused to approve the government’s plan — a largely symbolic act that nonetheless illustrated the opposition to Brexit in Scotland, where there is growing pressure for another referendum on independence.

But Britain is now on course to leave the European Union 10 months after the first date — March 29, 2019 — on which it was scheduled to do so. The real effects will not be felt before January 2021, however, because Britain will be in the transition period until then, still under the EU rule book.