LONDON—U.K. Prime Minister Theresa May’s Conservative Party largely held its ground in local elections, suggesting a continuing stalemate between her minority government and an opposition unable to capitalize on its travails.

After a difficult period for a government that is divided over Brexit and recently suffered a high-profile resignation over an immigration scandal, the Conservatives lost control of five councils and gained control of four in elections held in towns and cities across England.

But the main opposition Labour Party also lost control of two local authorities, as it gained two others, a performance not strong enough to suggest it would garner a parliamentary majority if a general election were called.The leaders of both parties hailed the elections as a success.

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The election results cap a particularly difficult week for the Conservative Party. A senior cabinet minister resigned on Sunday over the government’s treatment of long-term residents in the U.K. from the Caribbean, a scandal that further tarnished the party’s reputation.

And a year into negotiations over the U.K.’s departure from the European Union, Mrs. May is struggling to reach a consensus even within her government over the shape of Britain’s future relationship with the bloc. While Mrs. May wants to create a customs union that would soften the economic impact of Brexit on businesses, others who voted to leave the EU oppose her plan.

“When a government is in so much trouble, the opposition should be much further ahead than they are,” said Tim Bale, politics professor at Queen Mary, University of London. He said the public still doesn’t trust Labour to run the country and the economy and there are doubts about the competence of left-wing leader Jeremy Corbyn.

Labour, which revamped itself in the 1990s by reaching out to metropolitan voters, has struggled to retain its traditional working-class voters in postindustrial areas that were once the bedrock of its support. Many voters in these areas supported Brexit and haven’t felt the benefits of Britain’s economic recovery.

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With most of the results in Friday, Mrs. May lost council seats in areas including Plymouth in southern England and Trafford in Manchester, but held on to Westminster and Wandsworth, London strongholds that Labour had targeted.

The Conservatives won control of Barnet in north London, a council with a significant Jewish population. Labour has faced long-simmering accusations that it hasn’t adequately addressed anti-Semitism within the party, including harassment of Jewish lawmakers by members of the hard left. The party was once a natural place for the Jewish community in the U.K., but some longtime supporters have said they wouldn’t vote for a party that they consider to be hostile to the Jewish community.

The Conservatives also made gains in pro-Brexit areas including Peterborough and Basildon, where the anti-EU UK Independence Party previously had strong support. Support for UKIP, formerly led by Brexit campaigner Nigel Farage, melted down across the country, with the party having struggled to find a clear direction since the U.K. voted to leave the EU.

The centrist Liberal Democrats, which support staying in the EU, took control of the west London borough of Richmond from the Conservatives and made gains elsewhere, winning support from voters discontented with Mrs. May’s Brexit plans.

Write to Jenny Gross at jenny.gross@wsj.com

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