Care homes will be prevented from recruiting staff from abroad as part of an overhaul of rules to drive down net migration, Yvette Cooper has said.

In a change that will concern employers in the sector, the home secretary said providers should instead seek to employ foreign staff who have already come to the country or extend existing visas.

It is part of a preview of wider plans to be announced by Cooper on Monday designed to reduce net migration to the UK.

It has also emerged that the government plans to assess for deportation any foreign criminals who commit any crimes in the UK.

In a series of interviews on Sunday, Cooper said the government would not set a figure for net migration but would target recruitment in lower-skilled sectors.

Speaking to Sky News’s Sunday Morning with Trevor Phillips, Cooper said: “We’re going to introduce new restrictions on lower-skilled workers, so new visa controls, because we think actually what we should be doing is concentrating on the higher-skilled migration and we should be concentrating on training in the UK.

“New requirements to train here in the UK to make sure that the UK workforce benefits, and also we will be closing the care worker visa for overseas recruitment.”

Asked by the BBC’s Laura Kuenssberg where care homes would recruit staff from, Cooper said companies should recruit from a pool of people who came as care workers in good faith but had been “exploited” by unscrupulous employers.

“Care companies should be recruiting from those workers. They can also extend existing visas. They could recruit as well from people who are on other visas, who are already here. But we do think it’s time to end that care worker recruitment from abroad,” she said.

While Cooper declined to set a specific target for net migration, she said ministers believed changes to certain visas could result in “up to 50,000 fewer lower-skilled visas” over the next year.

At present, foreign criminals are only reported to the Home Office if they receive a jail sentence and only those given a year behind bars are usually considered for deportation.

Under the new arrangements, the Home Office will be informed of all foreign nationals convicted of offences – not just those who receive prison sentences – and will be able to use wider removal powers on other crimes, including swifter action to remove people who have recently arrived in the country but already committed crimes.

The overhaul will make it easier to remove those who commit offences, including violence against women and girls, street crime and knife crime, before the threat they pose escalates.

Chris Philp, the shadow home secretary, said he would support Labour’s idea of getting rid of care worker visas. Asked on the BBC’s Sunday With Laura Kuenssberg programme if he would support the plan, he said “yes, I would”.

On Monday, Cooper will present a government white paper – a document that sets out plans for future legislation – intended to notably curb net migration, as ministers try to respond to the local election success of Reform UK.

Nigel Farage’s party has focused much of its campaign work on the increase in net migration and successive governments’ failure to stop irregular crossings by asylum seekers across the Channel.

The Home Office will also introduce rules so that any foreign national placed on the sex offender register, regardless of sentence length, will be classed as having committed a “serious crime” with no right to asylum protections in the UK.

As part of the white paper, the government will update refusal policies and immigration rules to mirror these changes. This means if a person commits an offence while on a short-term visa, they will be refused if they make a fresh application.

Other proposals are expected to include new rules so that companies that repeatedly fail to show efforts to recruit UK-based staff, rather than recruit from abroad, could lose their right to sponsor foreign workers. Sectors targeted by the government include engineering and IT.

It is expected that work visas will be strictly time-limited for most jobs that do not need graduate-level skills.

Foreign students who have studied for degrees in the UK will face tighter tules over their right to remain after finishing university. Overseas workers will be expected to have a better understanding of English, but reported suggestions of A-level equivalent have been denied.

Cooper is under significant pressure to further reduce net migration. As well as winning control of 10 councils on 1 May, Reform, which is promising an effective freeze on most migration, is topping most polls of national voter preference.

While skilled visa numbers have already significantly reduced in the last few years, further hurdles to overseas recruitment could cause problems for industries such as care and hospitality.

Ministers also plan to introduce a Labour Market Evidence Group, made up of officials from industry and skills bodies, as well as from the government and the Migration Advisory Council (MAC). It would, the Home Office said, “inform understanding of where sectors are overly reliant on overseas labour and reverse underinvestment in domestic skills”.