Ministers should introduce electronic identity cards stating the right to live, work, claim benefits and use public services in Britain to address the concerns of leave voters about immigration in the event of a second referendum, a study has suggested.

The report from the Global Future thinktank, backed by the remainer peer Andrew Adonis, claimed the cards could be a key plank of any future campaign to persuade anxious voters that the UK did not have to leave the EU.

Under the proposal, electronic ID cards would be compulsory for anyone staying in the UK for more than 90 days. They would be used to claim entitlements and access public services, but could restrict those without the right to do so.

The government could then use the data to target extra funding for areas experiencing increases in immigration, although the report acknowledged there may be some privacy concerns and said the information must be anonymised and protected from abuse.

The thinktank also suggested setting up a “strengthening communities fund” underpinned by a £2bn-a-year investment in services and infrastructure to address the impacts of immigration, including increasing language provision and integration.

It called for a fairer labour market with Swiss-style enforcement squads to target unscrupulous businesses, and new protections for British workers, including rules to ensure they had the first chance to apply for new jobs.

Lord Adonis, who has visited the 100 constituencies with the highest proportion of leave voters, said: “These policies are practical, actionable solutions to immigration that are already being deployed across Europe.

“I believe strongly that they will help to persuade voters that the best way to take back control is to stay in the EU and get serious about immigration and welfare enforcement - so let’s do that instead of trashing our economy on the basis of a false choice.”

Theresa May interpreted the result of the Brexit vote as a clear instruction to end free movement, making it one of her red lines. The Global Future report suggested the public was more concerned about keeping out criminals and those who did not play their part in British society than ending all immigration.

The public also wanted to ensure jobs were protected and public services did not suffer as a result of growth in numbers, according to the report. The UK is the only EU member state not to have some form of identity card system.

Peter Starkings, the managing director of Global Future, said: “Free movement has been good for Britain – it’s boosted our economy, created jobs and helped millions of Brits live, work and study across Europe. Throwing it all away is terrible mistake that will damage Britain and deepen the very burning injustices the prime minister has promised to address.

“This report sets out a better way – control free movement so that it works for Britain, addressing public concerns and allowing us to maintain the close trading relationship with Europe that people want.”