British Prime Minister Theresa May has assigned a team of ministers with cutting down immigration, including through a “targeted visa system”, according to a government document published on Tuesday.

Curbing immigration influx was a target set by May’s predecessor David Cameron, but which the government has failed to meet. Net migration is currently running at more than three times that level.

The immigration taskforce, chaired by May and featuring 12 other ministers including the three leading Brexit campaigners Boris Johnson, David Davis and Liam Fox, has been asked to deliver annual net migration in the tens of thousands.

Setting out the terms of reference for the taskforce, the government said the target would be delivered by “implementing domestic measures to control migration; ensuring an efficient and targeted visa system and making it harder for illegal immigrants to stay in the country”.

The taskforce existed under Cameron, but its previous terms of reference did not mention a visa system.

May’s government has so far given little away about its plans for Britain’s future relationship with the European Union following a June vote to leave the bloc, but has been clear that controlling immigration is a key voter demand.