Think tank, British Future, which studies integration and identity, suggests that EU nationals should be offered permanent residency if they are already living in the UK, before Article 50 is triggered.
Its report on an independent inquiry looking into the status of EU nationals in the UK after Brexit calls on the government to clarify its position on what rights the 2.8 million Europeans living in the UK will have once Britain leave the European Union.
As part of its raft of proposals, the report wants the UK's Home Office to streamline applications for British citizenship, making it easier and cheaper by capping the cost of applying for permanent residence.
"EU nationals working in the UK and making a contribution are anxious about what happens to them when Britain leaves the EU. They need to know about their future rights to live and work here. Everyone agrees, this needs to be resolved quickly and fairly. Our inquiry now has practical recommendations for how to do it," Owen Tudor, TUC head of EU and international relations said.
"This shouldn't be a matter for negotiation. The Prime Minister should make the first move to unblock this ghastly uncertainty. It is morally right and pragmatically sensible," Tudor said.
Both Leave and Remain MPs contributed to the major inquiry into the future of EU citizens in Britain after Brexit, as fears are exacerbated about a "surge" in the number of EU migrants travelling to the UK before Article 50 is triggered.
"We determined that the triggering of Article 50 should be the cut-off date, after which EU citizens moving to the UK would not be entitled to stay permanently after Brexit. This would limit any 'pull factor' for EU citizens not already in the UK," Gisela Stuart, chair of the inquiry said.
Around 2.8 million EU citizens live in Britain, where it costs around US$1,262 for international migrants to apply for naturalization — the bureaucratic process of obtaining British citizenship.
Britain's Supreme Court will now decide whether Theresa May has the power to trigger Article 50 using a Royal Prerogative, sidestepping the UK Parliament.