EU citizens living in the UK would be stripped of their freedom of movement, housing and social security rights by Home Office legislation introduced to regulate immigration following Brexit, a parliamentary report has warned.

Despite repeated government reassurances that their privileges will be protected, a study by the joint committee on human rights (JCHR) concludes that more than 3 million Europeans living in Britain would be left in legal “limbo”.

The cross-party committee, whose members are drawn from the Commons and the Lords, argues that EU citizens’ rights should be protected by primary legislation rather than reliant on statutory instruments approved by ministers at a later date.

The JCHR also cautions that Irish nationals’ rights, guaranteed by separate common travel area agreements, would be “diminished”. Their ability to bring in a spouse from a non-EU state, for example, would be limited, the report says.

To prevent EU citizens being exposed to such uncertainty, the committee has drafted amendments to the bill – about to enter its report stage – to ensure rights are protected.

“Removing their rights without a legislative alternative in place raises significant human rights issues which the wide statutory instrument-making powers … do little to satisfy,” the report says. Without the necessary protections, the bill could leave individuals in a precarious situation over such issues as “housing, social security and property rights”.

The Labour MP Harriet Harman, who chairs the JCHR, said: “Human rights protections for EU citizens must not be stripped away after Brexit. EU citizens living in this country right now will be understandably anxious about their futures. We’re talking about the rights of people who have resided in the UK for years, decades even, paying into our social security system or even having been born in the UK and lived here their whole lives.

“When it comes to rights, promising that everything will be worked out in the future is not good enough, it must be a guarantee, which is why the committee have reinserted rights guarantees back into the wording of the bill.”

The report voices concerns that the government’s proposed EU citizen registration scheme post-Brexit does not provide physical proof of status. “Getting this right is extremely important considering the similarities of some of these concerns with problems that have arisen with the treatment of the Windrush generation,” the report says.

The JCHR fears that vulnerable people risk missing the registration deadline because of difficulties finding out about and accessing the EU settlement scheme. Their rights should not depend on registration within a specific time limit, the report says.

EU citizens have until 31 December 2020 to make an application under the scheme. In January, the home secretary, Sajid Javid, told the committee: “We have given unilateral assurances to EU nationals and their family members resident in the UK that they can stay if the UK leaves the EU without a deal.

“Although future policy for social security coordination is yet to be decided, the government has been clear that EU citizens and their family members in the UK at the point of exit will continue to have broadly the same access to benefits and services as now.”

A Home Office spokesperson said: “The government has already committed to protecting the rights of the millions of EU citizens living in the UK.

“We want them to stay and, whatever the outcome of the ongoing discussions about our exit from the EU, we will protect their rights and ensure they get the UK immigration status they need.

“The EU settlement scheme is designed to be as simple and straightforward as possible and during testing more than 200,000 people have applied. Today we launched a nationwide marketing campaign to encourage EU citizens to apply for the scheme, with other activity planned over the next two years to ensure people understand what they need to do.”