Tens of thousands more UK citizens applied for citizenship in other EU countries in the 12 months after the Brexit vote than in the previous year, according to data obtained by the BBC.
Ireland received by far the most applications for dual nationality.
But for all the countries that had data covering July 2016 to June 2017, applications have more than doubled.
In countries which had data only for calendar years, there was a sharp rise from 2015 to 2016 as well.
Among well-known UK citizens to apply for citizenship elsewhere in Europe is the Oscar-winning actor Colin Firth - it was confirmed last week that his application for Italian citizenship had been successful.
Yes, even Mr Darcy is feeling flustered.GETTY IMAGESBritish actor Colin Firth (pictured with his Italian wife) is now an Italian as well as a British citizen
Reality Check and Radio 4's More or Less contacted all EU countries to ask about the number of citizenship applications they had received from British people, before and after the referendum in June 2016.
It has not been possible to get full figures for every country, but the data we have compiled (reproduced at the end of this article) shows just how many people are taking precautionary steps in case the Brexit negotiations fail.
In the 12 months before the referendum, 25,207 Britons applied for Irish passports; in the 12 months directly after the vote that number rose to 64,400.
In other countries around the EU - Sweden (from 969 to 2,002), Denmark (from 289 to 604) and Poland (from 152 to 332) for example - the number of applications also more than doubled.
Then there are countries where data is made available in slightly different ways.
In Germany it comes state by state - so in Berlin there were 60 applications from British citizens in the year before the referendum, and 810 in the year after.
France, meanwhile, provides figures on a calendar year basis, and again the increase is clear - there were 385 applications in 2015, rising to 1,363 in 2016, and rising further to 2,129 in the first eight months of this year.
There is no precise way of knowing why people make citizenship applications when they do, but it seems safe to assume that political circumstances play a role.
In Ireland, for example, where monthly figures are available, the highest number of applications so far came in March, April and May this year - in the period just before or just after the British government triggered Article 50 and the countdown to the UK leaving the EU.
Roughly a million UK citizens already live elsewhere in the EU, and many more in the UK have the right to apply for citizenship in other EU countries. Since the referendum they have been doing just that in record numbers.
Of course this is not simply a one-way street. There are more than three million EU citizens living in the UK who are equally worried about their status post-Brexit.
And again, the number of citizenship applications in the UK is striking. In the 12 months before the UK voted to leave the EU, 15,871 people from EU countries applied; in the 12 months after it was 28,502.
Perhaps these figures don't come as a surprise.
But they are a reminder of why the issue of citizens' rights is at the centre of the current Brexit negotiations - and why all sides say it is a priority to resolve.
Brexit often seems to be about complex and distant concepts. But these are real people, worried about the future for themselves and their families.
Additional reporting by Phoebe Keane for Radio 4's More or Less, Tamara Kovacevic, Bethan Morrish, Joey D'Urso and Robert Cuffe.
You can hear more about these statistics on More or Less on BBC Radio 4 at 16:30 on Friday, 29 September or on BBC iPlayer Radio.
Data in full
These are all the figures from countries that were able to give us pre-referendum and post-referendum figures for passport applications by UK citizens.
These are the figures comparing the number of applications in the whole of 2015 with those for the whole of 2016.
The figures for Austria, Belgium, Germany and Italy are only successful applications as opposed to all applications.
The figure for Slovenia is for all people who applied for citizenship in the UK, not necessarily just UK citizens.
We did not receive data from the remaining six EU countries.