The problem is that some insurers will lose their automatic licence to provide payouts - such as annuity payments – in other European countries, if the UK leaves the single market in 2019.
See also: What is the best country for expats?
This is because they will lose the "passporting rights" that allow them to offer cross-border insurance, unless a new arrangement comes into force to prevent that.
According to the Association of British Insurers (ABI), this could affect millions of insurance and pension contracts.
ABI director general Huw Evans said: "Without a resolution, insurers will face a choice between breaking their promise to customers or risk breaking the law. It must not come to this."
Who is affected
News of this danger to their private pension payouts is another blow for worried British expats, who only recently discovered that they look set to keep annual increases in the state pension and still get their healthcare paid for after Brexit.
Robert Turner, a retired teacher living in the French Alps, said: "It's a very worrying time for people like me.
"There is so much uncertainty, some of my friends are convinced they are going to have to give up on their European retirement dream and are already making plans to return to the UK."
But older Britons living in other European countries are not the only ones who would be affected if no post-Brexit deal on this is reached.
People living in the UK and receiving a pension from the EU could also be hit should negotiations to prevent this fail.
What is being done
The Chair of the Treasury Select Committee Nicky Morgan has written to the Chancellor of the Exchequer asking about possible solutions.
"The possibility that UK providers may not be legally able to pay out pensions or insurance contracts to citizens in the EU – including UK expats – is a stark example of the consequences of a 'cliff edge' Brexit," she said.
"Both the UK and the EU have a strong mutual interest in resolving this problem, in line with their shared objective of a smooth and orderly Brexit."
Fortunately, hopes are high that a deal can be attained now the issue has been flagged.
Tom McPhail, pensions expert at adviser Hargreaves Lansdown, said: "Given the extent to which European regulation and legislation already sets the agenda for domestic UK regulation of financial services, it shouldn't be too challenging to reach an accommodation whereby business can continue as usual.
"Nevertheless the ABI is right to highlight the risks of not making sure a solution is identified and implemented in a timely manner."