The Remain and Leave campaigns have been urged to set out their position on the future of EU migrants already in the UK and ex-pats living in Europe in the event of Brexit.
Prominent think-tanks and campaign groups have warned there is significant uncertainty about how citizens from the bloc currently living in Britain would be affected by a Leave vote in the referendum in June.
They claim the picture is also unclear in relation to Britons living in other EU countries.
The Institute of Directors, New Europeans, Migrant Voice, the Joint Council for the Welfare of Immigrants, Open Europe, Policy Exchange, British Future and Migration Watch - which campaigns for tighter immigration restrictions - joined forces to call for campaigners on either side to clarify their position.
In an open letter, they said the Government should make clear its policy would be to protect the rights of EU nationals living and working in the UK and seek reciprocal arrangements for British citizens in other EU countries.
They argued future changes should not apply "retrospectively" to those currently exercising free movement rights, saying: "Both current EU migrants in Britain and British migrants living in other EU member states should be able to continue to live and work in those countries."
Veronika Susedkova, 29, a Czech charity worker from Yorkshire, said: "The uncertainty of this referendum feels to me like British weather: you don't know what's coming until it's there, it changes very suddenly and you can't do anything about it."
An online poll of 1,018 UK adults also found 83% of respondents think the Government should clarify the position before the referendum.
Asked whether existing EU migrants should be able to remain in the UK in the event of Brexit, around a quarter of people said they did not know and of those who answered, two-thirds (67%) think they should be allowed to stay, with around a quarter (26%) feeling they would have to leave.
The letter sparked fresh hostilities between the opposing camps.
Will Straw, of Stronger In, said: "As part of the EU, millions of Brits live and work freely across Europe and many more aspire to do so in the future.
"If we left, that automatic entitlement could end, throwing their future into doubt. That would mean enormous disruption for many Brits - on top of the risk of job losses and prices rising that leaving would entail.
"No-one knows what Britain's future would look like if we left. Leave campaigners have so far refused to set out their vision of what leaving would actually mean for Britain or for Britons living across the continent.
"What's certain is that if we pulled out of Europe and stopped Europeans from coming to work in Britain, we would lose our access to the world's largest free trade area, costing us jobs and pushing up prices in this country. For most Brits, that's a price not worth paying."
A spokesman for Vote Leave said the rights of EU citizens living in the UK "will not be threatened or undermined" if the country votes for Brexit.
"There would be no question of EU citizens being removed from the UK because of the referendum result," he said.
"Similarly, UK citizens in the EU will not be deported as their rights will be protected.
"We deeply regret that some pro-EU voices are preying on the fears of those living in the UK and abroad, rather that engaging in an honest debate."
A Government paper published in February said UK citizens living, working and travelling in the other 27 EU member states "currently enjoy a range of specific rights to live, to work and access to pensions, health care and public services that are only guaranteed because of EU law".
It added: "There would be no requirement under EU law for these rights to be maintained if the UK left the EU.
"Should an agreement be reached to maintain these rights, the expectation must be that this would have to be reciprocated for EU citizens in the UK."