LONDON (Reuters) - British Prime Minister Rishi Sunak on Monday promised to introduce a legal cap to curb immigration levels if re-elected, taking aim at one of the main issues facing the country ahead of next month's national vote.

His Conservative Party, which is trailing opposition Labour in polls, said that if the party returned to power, lawmakers would vote to set immigration levels, an issue that has dominated Britain's political debate for more than a decade and played a role in the Brexit referendum.

"By capping migration numbers each year, we will ensure that public services are protected and housing is not overburdened, while still bringing the skills our businesses and NHS (National Health Service) need," said the party, which is predicted to be heading towards its biggest election loss in over a century.

Sunak brought in new rules this year to cut legal migration, including barring international students from bringing in family members and increasing the salary threshold for skilled worker visas.

Annual net migration to Britain fell to 685,000 in 2023 from a record high of 764,000 in 2022.

"We have taken bold action to cut the number of people coming to this country. The plan is working but migration levels are still too high, so we are going further," he said in the statement.

The Conservative government's flagship policy to send asylum seekers who arrive in Britain without permission to Rwanda for processing has faced legal and parliamentary obstacles, and now hinges on the party winning the election.

Alongside the state of the country's health service and its economy, the issue of immigration and asylum was cited by Britons as among the most important problems in Britain at present, according to a YouGov tracker.

(Reporting by Muvija M, editing by Deepa Babington)