David Cameron and Theresa May have briefed the cabinet that they remain committed to the Tory ambition of ensuring net migration is cut to the tens of thousands of people.

The prime minister and the home secretary outlined their plans at a meeting of the cabinet, which focused on the government’s legislative agenda that will be outlined in the Queen’s speech on 27 May.

Ministers, who held a meeting of the political cabinet attended by Boris Johnson before the main cabinet, were also briefed by Andrew Parker, the director general of MI5, and by Robert Hannigan, the director of GCHQ. It is understood that the briefing focused on UK security threats rather than on the plans to reintroduce the “snooper’s charter”.

Cameron is understood to have told the cabinet that he will show his determination to keep his word on Europe by publishing the bill to deliver an EU referendum the day after the Queen’s speech. The Queen will also announce that the government will introduce bills to abolish the Human Rights Act, which will be replaced by a British bill of rights; a schools bill to make it easier to allow failing or “coasting” schools to be turned into academies; and an enterprise bill to save at least £10bn by cutting red tape for companies.

In addition to outlining to ministers the list of parliamentary bills, George Osborne, the chancellor of the exchequer, also gave the cabinet an economic update, while the prime minister and home secretary outlined their determination to cut net migration to the tens of thousands. The prime minister’s spokesman said of the policy: “That remains absolutely the case and the update very much reflected that.”

Cameron and May faced criticism in the run-up to the election when the coalition missed its net migration target. The prime minister, who had delivered a “no ifs no buts” pledge in 2011 to deliver the target, was embarrassed a few weeks before the election when official figures showed that net migration to Britain was 298,000 last year. This meant that the net migration figure was 54,000 times higher than when the Tories made their pledge in 2010.

But the Tories recommitted themselves in their general election manifesto to meeting the target, although they described it as an ambition. The manifesto blamed migration from the EU for its failure to meet their objective.

“As a result, our action has not been enough to cut annual net migration to the tens of thousands,” the Tory manifesto said. “That ambition remains the right one. But it is clearly going to take more time, more work and more difficult long-term decisions to achieve. Continuing this vital work will be our priority over the next five years.”

Downing Street said the prime minister’s EU reform plans, in which he will seek to limit access to in-work and out-of-work benefits to EU migrants, will be crucial in meeting the “ambition”. The prime minister’s spokesman said of the prime minister and home secretary’s briefing on immigration: “This brings together issues around skills and welfare reform to ensure that people can progress through the labour market and that work always pays, the measures around border and border force-related issues. Alongside that you also have the changes the prime minister and others seek in relation to the EU.”

The No 10 spokesman played down the significance of the disclosure that Deutsche Bank is reviewing whether to move parts of its operations to Germany if the UK votes to leave the EU. The FT reported that the bank, which employs 9,000 people in the UK, has established a working group to plan for a potential exit from the UK.

The prime minister’s spokesman said: “Some of these reports are considered in terms of this issue around certainty. The prime minister is the person who is providing certainty. He is the one that has the very clear plan to go and renegotiate our relationship with the EU and then put that to the British people.”