It’s By-election Day in the U.K. What Does That Mean?

One of the last things Britain’s prime minister, Rishi Sunak, needs right now, while he’s trailing in the opinion polls as the economy stalls, is a test of his electoral popularity.

But on Thursday, he faces three contests, as voters in different parts of England select replacements for a trio of lawmakers from his Conservative Party who have quit Parliament, including former Prime Minister Boris Johnson.

The votes, known as by-elections, happen when a seat in the House of Commons becomes vacant between general elections. In the British system, every elected lawmaker represents a district, so when they quit, those voters decide who will succeed them.

Hanging over the contests is the poisoned legacy of Mr. Johnson, who angrily quit Parliament after lawmakers ruled that he had lied to them about Covid-lockdown-breaking parties in Downing Street.

Because the government will not change whatever the outcome, voters often use such by-elections to register unhappiness with their political leaders. And with inflation and interest rates high, labor unrest boiling and the health service struggling, Mr. Sunak’s Conservatives are braced for the possibility of losing all three contests.

That would make Mr. Sunak the first prime minister to suffer a triple by-election defeat in one day since 1968. It would also stoke fears among Conservatives that, under his leadership, they are heading for defeat in a general election expected next year.

But by-elections are unpredictable, so nothing is certain on this so-called super Thursday. And so low are expectations for the Conservatives that even winning one would be a welcome relief for Mr. Sunak.

Here’s where voters are casting ballots:

Uxbridge and South Ruislip

This is the seat vacated by Mr. Johnson, and it lies on the fringes of London, the capital. Although the inner areas of the capital tilt to Labour, the main opposition party, outer London, with its suburbs and larger homes, is much better territory for the Conservatives. Mr. Johnson’s majority in the last general election was relatively modest at 7,210 votes, and the scandal-hit former prime minister is a divisive figure, so Labour hopes to win here.

But the Conservatives see an opening in a plan to expand an ultralow-emissions program to areas including Uxbridge and South Ruislip. The expansion, pressed by London’s Labour mayor, Sadiq Khan, would cost those driving older, more polluting cars. Conservatives are campaigning against the expansion. The Labour candidate for the area has also said he is against the expansion, though Labour’s leader has not taken a stand.

Selby and Ainsty

The contest in Selby and Ainsty, in Yorkshire in the north of England, is another aftershock of recent political turbulence because the lawmaker who quit, Nigel Adams, was a close ally of Mr. Johnson’s. He resigned after not being awarded a seat in the House of Lords, as he had expected. This is a scenic part of northern England but also one with a mining history, and Labour will be hoping it can snatch the seat.

That would send a powerful signal that the party is returning to popularity in the north and middle of England — areas it once dominated but where it lost out in the 2019 general election. Yet, it’s a tall order. If Labour can succeed in Selby and Ainsty, where the Conservative majority in 2019 was 20,137, that would set a record for the size of a majority overturned by Labour in a by-election. So victory for Labour here would suggest it is well on course for a general election victory.

Somerton and Frome

Instead of Labour, the smaller, centrist Liberal Democrats are seen as the main challengers to the Conservatives in Somerton and Frome, in the southwest of England.

The vote follows the resignation of David Warburton, who quit after admitting that he had consumed cocaine. The Lib-Dems have a strong tradition of success in this attractive, mainly rural part of the country, and they held this electoral district until 2015.

In the last election, the Conservatives won a big majority, 19,213. But since then, the they have suffered losses in some of their heartland areas in the south of England, the so-called blue wall, named after the party’s campaign colors.

At the same time, the fortunes of the Liberal Democrats have been revived considerably. This year, they performed well in elections in local municipalities, and last year, they stormed to victory in a by-election in Tiverton and Honiton, also in the southwest.