Votes will be cast across England on Thursday in local elections that will be a test of the popularity of Prime Minister Rishi Sunak, who has stabilized Britain’s politics but whose government remains unpopular in the face of surging inflation, sluggish economic growth and labor unrest.

These votes will not affect the national Parliament that gives Mr. Sunak his power: Members of Parliament face the public every five years or so in a general election. The date is flexible but one isn’t expected until next year.

But Thursday’s voting could offer important clues about whether Mr. Sunak, whose Conservative Party trails the opposition Labour Party in opinion polls, can turn things around.

At stake are seats for around 8,000 representatives in lower tiers of government: municipalities that control services like garbage collection and construction permitting and raise taxes, within strict constraints, on residential property.

It’s not an infallible guide to national sentiment. Turnout will be far lower than at a general election and parochial issues like planned housing developments could sway some races.

Still, this may be the largest public vote between now and the next general election, and it’s fought across most of the areas likely to determine the next British government, with national issues often prominent in campaigning.

Recent surveys show Mr. Sunak cutting into Labour’s lead, though it remains in double digits. So he retains hopes of snatching an unlikely fifth consecutive general election victory for the Conservatives.

Keir Starmer, Labour’s leader, needs a decent result to sustain his hopes of becoming the next prime minister. Despite moving his party close to power, he has failed to excite voters.

The local elections will indicate how Labour’s polling lead and Mr. Sunak’s polling progress translate into real votes.

The elections on Thursday take place across much — but not all — of England. Scotland and Wales aren’t voting, and Northern Ireland has local elections on May 18.

Up for grabs are seats for representatives in 230 municipalities. The last time these seats were contested was in 2019, when Parliament was gridlocked over Brexit and the two main parties were about equally unpopular. Many big cities are voting (London excepted) but so are more rural areas.

Both main parties hold a lot of these seats, but the Conservatives are defending the most — around 3,500 — and polling suggests they will lose plenty.

How many is the key question: The parties traditionally seek to massage expectations. Greg Hands, the chair of the Conservatives, has talked of estimates that his party could lose 1,000 seats — a high number that some analysts think he inflated in an effort to portray lower losses as a triumph.

Some the most closely watched votes will be in so-called red wall areas in northern England and the Midlands. These deindustrialized regions used to be heartlands of the Labour Party. Mr. Sunak’s predecessor but one, Boris Johnson, fought a pro-Brexit general election campaign in late 2019 that won many of them for the Conservatives.

With support dwindling both for the Conservatives and for Brexit, Labour hopes to regain some former strongholds, for example in northeastern England in areas like Middlesborough and Hartlepool.

In the south, analysts will watch how the Conservatives perform in their traditional strongholds, prosperous towns like Windsor and Maidenhead, now sometimes known as blue wall areas. Here, Mr. Johnson alienated anti-Brexit Conservative voters, allowing independent candidates and a centrist party, the Liberal Democrats, to make gains. Mr. Sunak hopes his more technocratic style has arrested that slide.

Some results should emerge overnight — the northern city of Sunderland, for instance, prides itself on having all its votes counted just hours after the polls close, at 10 p.m. local time — but many places start counting the next day. There won’t be a reliable picture of votes across England until later on Friday.

Earlier this year, when Mr. Sunak’s leadership looked shaky, these elections seemed like a potential trigger for a leadership crisis and a comeback opportunity for Mr. Johnson, whose own fall was accelerated by local election losses last year.

Since then, Mr. Sunak has struck a post-Brexit deal with the European Union on Northern Ireland, and stabilized the economy after upheavals under Liz Truss, Mr. Johnson’s short-lived successor. By contrast, Mr. Johnson is embroiled in an inquiry into whether he lied to Parliament about lockdown-busting parties during the pandemic.

So Mr. Sunak’s position looks secure for now. But a bad result could demoralize party workers, shake confidence in his prospects, embolden his critics and confirm expectations that he will postpone calling a general election until late next year (it must take place by January 2025). A better-than-expected result for the Conservatives would strengthen Mr. Sunak and increase pressure on Mr. Starmer.

If the Conservatives do suffer, the prime minister has one big thing going for him: timing. On Saturday, all the British media’s attention will shift to the pomp and pageantry of the coronation of King Charles III.