Since the UK introduced a points-based visa system post-Brexit, ministers have talked tough on immigration while allowing employers to look abroad to plug workforce gaps and encouraging universities to bring in overseas students.

Last week Conservative MPs demanded urgent action after it emerged that net migration – the number of people immigrating minus the number emigrating – was a record-breaking 745,000 in the calendar year 2022.

This unusually high level was due to a combination of humanitarian schemes for Ukrainians and Hongkongers, as well as international students and work visas.

Conservative sources admit the government will find it next to impossible to achieve its manifesto promise of cutting migration to below 2019 levels before the next election.

What are the options to bring down net migration?

James Cleverly, the new home secretary, is assessing a number of options to cut migration figures, which have been on the table for months.

The government has already announced plans to clamp down on dependants of students arriving in the UK, which Sunak has claimed is “the single toughest measure that anyone has taken to bring down the levels of legal migration in a very long time”.

It is understood that Cleverly is expected to present a series of additional measures within weeks to try to introduce some control to net migration figures.

What about cutting the shortage occupation list?

Ministers are looking closely at dropping the current list, which allows employers to pay wages that are 20% under the UK going rate.

The list contains dozens of jobs across a wide range of industries and has been criticised for repeated additions in recent years.

The Migration Advisory Committee urged the government to scrap the shortage occupation list earlier this year because of concerns that it was increasingly being used by companies in low-wage sectors to hire cheap foreign labour instead of recruiting domestic workers.

However, the list has been defended as vital by employers, the Treasury and the Department of Health, which argue that scrapping it would damage the economy and hamper pledges to cut the NHS waiting list.

Could ministers cap the number of work visas issued to overseas workers?

It is a move that was broadly supported on Tuesday by the immigration minister, Robert Jenrick, after demands from hard-right MPs.

However, migration experts have warned that visa caps can frustrate employers and hinder economic growth, and could damage the health service at a time when the government is trying to cut waiting lists.

Of the 189,000 skilled worker visas granted to both EU and non-EU citizen applicants in the year ending June 2023, more than 60% went to workers in the health sector.

What about minimum annual salary requirements?

These measures – which would restrict visas to pay above a minimum level to ensure a level playing field with domestic workers – are being actively examined by ministers.

The level of pay is being publicly debated by former ministers. Suella Braverman, the former home secretary, has argued that the level should be £45,000.

Writing in his Daily Mail column, the former Conservative prime minister Boris Johnson said the minimum income for most migrant workers should be increased to at least £40,000. Reports have claimed that the government is examining a possible level of £35,000.

Could the government restrict the ability of foreign workers to bring in family members and spouses?

Further controls are widely expected to be introduced by the government. But this could well damage the government’s ability to attract workers, particularly in the care sector, experts have warned.

Prof Brian Bell, who chairs the Migration Advisory Committee, told the Observer: “You can’t encourage enough British people to do the work in social care because it’s so badly paid. If you make it harder for migrants to come in on the route … that might begin to reduce the number who are coming in. That will reduce net migration, and so the government might be happy with that.”