LONDON — Leaving the European Union would be an act of ‘‘economic self-harm,’’ British Prime Minister David Cameron said Thursday during a televised grilling that saw him challenged on the emotive topic of immigration and accused of scaremongering about the impact of quitting the 28-nation bloc.

Three weeks before British voters decide whether to stay in the EU, Cameron was pressed on the repercussions for immigration, security, and the economy as he fielded questions from a journalist and audience members during a lively Sky News program.

Cameron’s Conservative government says it aims to reduce net annual migration to less than 100,000 — but last year it was more than 330,000, roughly half of it from other EU nations.

He insisted that Britain can use curbs to welfare benefits and other measures to control migrant numbers while remaining in the bloc, even though citizens of all EU nations have the right to live and work in other member states.

‘‘There are good ways of controlling migration and there are bad ways,’’ Cameron said.

‘‘It would be madness to try to do that by trashing our economy and pulling out of the single market.’’

The referendum campaign is growing increasingly heated as widely varying polls suggest an unpredictable result.

Associated Press