LONDON — In a tumultuous week for British politics, the contest to become leader of the centrist Liberal Democrats was doubtlessly the undercard, featuring two little-known lawmakers who disagreed politely and are not within a sniff of 10 Downing Street.

But despite being in the shadow of Boris Johnson, the Conservative Party firebrand, the new leader of the anti-Brexit Liberal Democrats, announced on Monday as Jo Swinson, a 39-year-old Scottish lawmaker, could nevertheless soon become a kingmaker in Britain’s topsy-turvy political scene.

Ms. Swinson’s victory drew far less notice than the Conservative leadership race, given that the next leader of that party, most likely Mr. Johnson, will also become prime minister. Voting among dues-paying Conservative members closed at the end of Monday, and the winner will be announced on Tuesday morning.

If Mr. Johnson prevails, he will inherit perhaps Britain’s greatest peacetime crisis — the vote to leave the European Union — as well as an escalating standoff with Iran. But he will have to navigate those crises with a razor-thin working majority in Parliament, and with fierce doubts eating away at support within his own party.