Some 190,000 British pensioners are currently receiving healthcare in different EU countries at a cost of around £500 million a year.
Some 190,000 British pensioners are currently receiving healthcare in different EU countries at a cost of around £500 million a year for Britain's state-run National Health Service (NHS).
But the Nuffield Trust study said this could rise to £1 billion (1.1 billion euros, $1.3 billion) if the pensioners returned due to higher health costs in Britain compared to other EU countries.
If the NHS needed to host people currently receiving care abroad it would also have to create additional bed spaces -- the equivalent of two extra hospitals.
Under a reciprocal scheme, British pensioners have the right to go to any EU member state and receive the same health rights as the local population.
The Nuffield Trust urged Brexit negotiators to try to secure a deal that would mean that expats continue to receive care in the countries they reside in.
"The NHS and social care were already under pressure from tight funding settlements and growing staffing problems well before the EU referendum last year," the report's author Mark Dayan said.
"But if we handle it badly, leaving the EU could make these problems even worse," he said.
Asked about the issue during an election campaign stop in Plymouth in southwest England, British Prime Minister Theresa May said: "I want to see reciprocal arrangements so their rights are protected".
The report also warned about the impact of lower immigration as the NHS is heavily reliant on being able to recruit medical staff from the EU.
Mark Porter from the British Medical Association said: "Politicians must keep the health service and its patients at the forefront during Brexit negotiations and reduce the impact that leaving the EU will have on health and social care across the UK".