Theresa May has indicated she will campaign in favour of Britain’s continued membership of the EU after describing the proposals tabled by the European council president as the “basis for a deal”.

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In a major boost to David Cameron, who laid the ground for a short referendum campaign to keep Britain in a reformed EU after Donald Tusk published his proposals, the home secretary said progress had been made in the negotiations.

“EU free movement rules have been abused for too long and EU law has stopped us deporting dangerous foreign criminals,” she said in a statement. “That is plainly wrong and it is encouraging that the commission has agreed with the UK that we should take action to address these two issues.

“So we have made progress and negotiations continue ahead of the February council. As the prime minister has said, more work needs to be done, but this is a basis for a deal.”

May’s statement means most of the cabinet heavyweights are now expected to line up behind the prime minister to campaign in favour of continued EU membership. Michael Gove, the justice secretary, and Boris Johnson, a member of the Tories’ political cabinet, are likely to join Cameron, the chancellor, George Osborne, and the foreign secretary, Philip Hammond, in campaigning to keep Britain in the EU.

Iain Duncan Smith, the work and pensions secretary, is likely to be the only heavyweight cabinet member campaigning to leave. He will be joined by Chris Grayling, the leader of the Commons, Theresa Villiers, the Northern Ireland secretary, and John Whittingdale, the culture secretary. Priti Patel, who attends cabinet as employment minister and first made her name as a member of the late James Goldsmith’s Referendum party, may also campaign to leave.

There had been fears in Downing Street that May might campaign to leave the EU after a hardline speech at last year’s party conference. She also feels bruised by the failure to meet the government target for net migration to drop below 100,000, blaming it on uncontrolled immigration from the EU.

In recent months, however, senior government sources had decided that May would, on balance, support UK membership of the EU. Her decision to opt into a series of EU security measures, after exercising the UK right to opt out of all measures, led them to conclude that it would be difficult for her to argue for exit.