Companies that refuse to comply with Labour’s plans for training British workers could be blocked from sponsoring visas for overseas employees, if the party wins the election.

On Sunday, Labour set out how it would bring net migration down by reducing the need for foreign workers.

The party said it would improve training for an initial four sectors including health and social care, construction, engineering and IT.

More detailed plans seen by the BBC show that Labour would make it more difficult to hire foreign workers in those roles, if the sectors don’t take “sufficient steps” to carry out workforce training.

A Labour government would also be able to “refuse” individual companies from sponsoring work visas if they believed the employer was not doing enough.

The four named sectors would each have a “workforce plan” drawn up by the relevant government department.

Those plans would detail how Labour believes that companies could best go about training up workers in Britain, and reducing reliance on overseas employees.

If ministers believed a sector was not engaging with the plan, then jobs within that industry could be removed from the shortage occupation list.

People who work in jobs on the shortage occupation list are able to apply for a skilled worker visa, to come and work in the UK.

If the jobs were removed from the list, Labour says that companies would be required to “recruit locally”.

A party source said the plan would be “very flexible” and indicated there could be special opt-ins for well-performing companies if wider sectors are sanctioned.

Graham Watts, chief executive of the Construction Industry Council, told the BBC that “putting arbitrary limits on skilled immigration” before workforce plans were given time to properly develop could “stifle economic growth”.

He said plans to train up more British workers would “mitigate the shortfall and ultimately provide growth” but warned that it “will not happen overnight”.

Martin Green, chief executive of Care England, a representative body for care providers in England, said it was a “cause for concern” that Labour’s plan would involve ministers making the key decisions.

He said the wider plan to boost training was “welcome” but called for an independent body to oversee decisions about potential sanctions.

A Labour party source said that the Migration Advisory Committee, an independent body that already exists and advises on policy, would also be advising on these plans.

Labour has spent months courting support from business ahead of the election, with shadow chancellor Rachel Reeves holding regular meetings with City leaders.

That culminated in a letter from more than 120 business voices endorsing the party earlier this month.

One source involved in orchestrating that charm offensive said these plans to potentially block overseas visas had not previously been mentioned.

Shadow home secretary Yvette Cooper told Sunday with Laura Kuenssberg that Labour wanted to see “significant changes in place” across the economy to reduce reliance on overseas workers.

But she added the party would not set a migration target because the Conservatives had “ended up being totally all over the place” when they did.

The Conservatives have also set out plans to reduce the number of visas available to migrant workers if they are returned to power.

MPs would get a vote on an annual migration cap, based on recommendations from the Migration Advisory Committee, under the Tory plans.

Reform UK has set out proposals to increase taxes on companies that employ overseas workers, to end what it calls the country’s “addiction” to cheap foreign labour.

Under Reform’s policy, firms would pay a higher 20% rate of National Insurance for foreign workers, up from the current 13.8%.

The Lib Dems have pledged to transfer powers over work visas, overseas students and asylum from the Home Office to other departments, and set up a new, arms-length unit to process applications quickly and correctly.