Labour will unveil a compromise position on immigration in its manifesto on Thursday that would not commit fully to free movement after Brexit but would expand the rights of migrants to bring family members to the UK.

Ahead of the manifesto launch, Jeremy Corbyn said he would want his government to allow “a great deal of movement” of people in a sign Labour would want a liberal immigration policy overall.

However, the Labour leader stopped short of saying free movement would be allowed to continue in its current form, arguing instead for immigration to help with shortages in the NHS and for an expansion of the rights of migrants to bring family members to the UK.

Speaking on Sunday on the BBC’s Andrew Marr Show, he said: “A lot of EU nationals have made their homes in this country and made a massive contribution to our society … many of those families have been through unbelievable stress. So they absolutely must have the right to remain and bring their families here.

“Also, there are also huge economic demands. There are 40,000 nurse vacancies in the NHS, partly because so many EU nationals have left. We have a shortage of doctors. We cannot exist in isolation.

“Therefore there has to be migration into Britain in order to maintain our economy and our services. That will be reflected in our policy that you see on Thursday.”

Pressed again on whether free movement would continue, Corbyn said: “There will be a lot of movement.”

The party’s 2017 manifesto said free movement would end at the point of Brexit. This election’s manifesto is not committed to carrying out Brexit, so the position will be that free movement would remain if the UK stays in the EU but it would be revised as part of any Brexit deal negotiated by Labour.

Any Labour-negotiated deal would be likely to adopt a regime that is very close to the current arrangements in order to maintain single-market access, making sure that expanded rights of family reunion are part of the offer.

A motion passed by the Labour conference argued for the UK to “maintain and expand” free movement, which its organisers intended to mean an expansion of free movement to apply to countries across the world.

However, Corbyn argued the movers of the motion only meant an expansion of family reunion rights.

“I agree with the principle there has to be the right of joining your spouse or whatever in this country,” he said.

The Tories have tried to make immigration a battleground issue, arguing that the Labour conference motion would mean open borders and immigration of 840,000 people a year to the UK.

Labour’s manifesto will make no such commitment to open borders and is likely to say that any new immigration regime with the EU would be negotiable as part of a Labour-led deal if Brexit goes ahead.

The position was thrashed out at Labour’s meeting on Saturday to determine the manifesto. Other major policies are expected to include higher income tax for those earning more than £80,000, reversing corporation tax cuts, bringing all free schools and academies under local authority control and a large programme of renationalising utilities, broadband, railways and the postal service. Labour is also expected to bring in a form of windfall tax on oil and gas companies and continue with plans to ask firms to hand 10% of shares to workers.

The party is not expected to go as far as putting all private schools into public ownership and seizing their assets, which was passed at conference, but it is likely to commit to closing tax loopholes that mean they get preferential treatment.

The party’s Brexit position had already been settled at conference, with Labour planning to negotiate its own Brexit deal and then hold a special conference to decide the party’s position before a second referendum within six months.

The Conservative party gave more details of its own plans for a post-Brexit immigration regime on Sunday, saying it would want migrants to be treated equally wherever they come from in the world, based on their skills.

Under the Tory plans, the vast majority of immigrants would have to have a job, apart from highly skilled scientists and entrepreneurs. The Conservatives would also restrict access to benefits for both EU and non-EU nationals so that migrants would have to wait five years before getting them.

The Tories would stop child benefit being sent abroad to support children who do not live in the UK and increase the annual cost for new migrants of accessing NHS treatment from £400 to £625.

Asked about the Conservatives’ immigration proposals, the security minister, Brandon Lewis, told Sky: “Anybody who’s already here and is part of the EU settled status scheme, their rights are protected, they are absolutely clearly protected and in place.

“This will be for new people coming from the EU once we’ve left the European Union under a future immigration system.”