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."
How we spend our pensions
How we spend our pensions
Figures from Saga show that the over 50s now account for the majority of money spent by Brits on travel and tourism. They have the time to spare, the money, and they are healthy enough to take on the world.
A poll from Abta found that in the wake of pension freedoms, 35% of people were considering cashing in at least part of their pension to travel. A separate study by Senior Railcard found that pensioners take an average of three holidays a year, plus two weekends away, and 17 day trips.
Research from Senior Railcard found that retirees eat out an average of three times a month. However, one in ten do so more than twice a week, and one in three people said that one of the first things they did when they retired was to go out for lunch with their friends.
Of course, just because retirees want to enjoy themselves, it doesn't mean they are happy to throw money away. The vast majority are keen to eat at lunchtimes, when a fixed lunch menu tends to be cheaper, and canny retirees are skilled at tracking down pensioner special offers too.
Figures from the Office for National Statistics show that on average nearly a fifth of the money spent by people aged 65-74 is on leisure. This includes everything from the cinema and theatre to golfing and gardening. They spent more on this than on food, energy bills and transport.
A report by Canada Life found that retirees are spending £4,279 a year on having fun - that’s more than £1,000 more than they spend on boring essentials, and is a 74% increase over the past ten years. It went on to predict that this trend was set to continue, and that pension freedoms would encourage people to spoil themselves a bit more in retirement
Pensioner property wealth is now over £850 billion, and all these family homes don’t look after themselves. The Senior Railcard survey put home renovations in the top 20 activities people got stuck into on retirement, and figures from ABTA found that almost a third of people who were considering raiding their pension pots under the new pension freedoms planned to spend the cash on their home. This seems like an eminently sensible investment - looking after what is undoubtedly their most valuable asset.
Unsurprisingly, while some pensioners are very well off indeed, others are struggling with debt. Figures from Key Retirement found that the average retiree has £34,000 of debt.
Most of this is mortgage borrowing - in many cases driven up by the number of people who unwittingly signed up to an interest-only mortgage. However, credit cards, overdrafts, and loans are also common. It’s why so many pensioners have used pension freedoms to access enough cash to pay their debts.
The day to day basics are swallowing up their fair share of pensioner cash too. On average, people aged 65-74 spend a third of their weekly income on essentials like food and bills - which is hardly living the high life.
The bank of gran and grandad has become an increasingly vital source of cash for families. According to Key Retirement, of those who release equity from their property, 21% of them use the cash to treat their children and grandchildren. This includes an average of £33,350 to help children get onto the property ladder, £6,000 to buy them a new car, £11,000 on family weddings, and £24,780 giving grandchildren a helping hand.
While retirees are quite rightly spending what they need to enjoy retirement, they are hardly all throwing caution to the wind, buying flash cars and spending the kids' inheritance.
Most expect to have something left over to pass onto their family after their death. Some 69% expect to leave property in their wills, and 75% expect to leave cash - according to Unbiased.co.uk - because while baby boomers know how to have fun - they also know how to save for the future.