If all the British pensioners who currently receive health care in other countries through European Union agreements had to return, caring for them would require the NHS to spend an extra £1 billion a year, according to a report from the Nuffield Trust.
The health charity said this is twice the amount currently spent for them to receive their care abroad.
Theresa May claims the NHS £1bn Brexit bill proves she was right to delay giving EU citizen rights
The Prime Minister said a reciprocal deal was needed which is "why it is so important we haven't just given those rights to EU citizens here in the UK".
During a visit to Plymouth, Mrs May said: "From day one as Prime Minister I've been clear that I want to ensure that we are supporting and looking after British people.
"If we look at people who are living in the European Union, I'm clear that I want to see agreement where their rights are protected.
"Of course, it is reciprocal for EU citizens living here in the UK.
We are looking after UK citizens living in the European Union
"But it is why it is so important we haven't just given those rights to EU citizens here in the UK.
"We are looking after UK citizens living in the European Union.
"I want to see reciprocal arrangements so their rights are protected and we can look after them.
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"As British Prime Minister, I have a care for the British people living in the EU."
Both Labour and the Lib Dems have said they would guarantee the rights of EU citizens in the UK ahead of negotiations.
Under the current EU reciprocal 'S1' scheme, British pensioners have the right to go to any other EU member state and receive the same health care rights as the local population. The agreement protects around 190,000 British pensioners.
A think tank claimed the cost to the NHS of pensioners returning from the EU could be £1bn a year
The Nuffield Trust report also says that if the NHS needed to care for those who currently receive care abroad, it would need a significantly higher number of hospital beds – the equivalent to two new hospitals.
And it highlights how health and care services are dependent on EU migrant workers.
Report author Mark Dayan, policy and public affairs analyst at the Nuffield Trust, said: "The NHS and social care were already under pressure from tight funding settlements and growing staffing problems well before the EU referendum last year.
Mrs May claimed she was protecting the rights of Brits living in the EU
"But if we handle it badly, leaving the EU could make these problems even worse, given the potential impact on both the strength of the UK economy and the supply of overseas staff to both health and social care services.
"It is possible that extra funds could be found for the NHS from any cancellation of Britain's EU membership fees – but whether or not these benefits will outweigh the significant staffing and financial costs Brexit may impose on already stretched services remains to be seen.
"That depends largely on the NHS being recognised as a significant priority as we enter some of the most important negotiations in Britain's history."