Applications for French nationality by British citizens living in France more than tripled last year compared with 2015, according to interior ministry figures.

The figures, obtained by Le Monde newspaper, showed 1,363 Britons in France applied to become French citizens in 2016, compared with 385 the previous year – a 254% increase.

The news came after Germany’s federal statistics bureau last week said a record 2,865 Britons took German citizenship last year, up 361% on 2015. The bureau said the link to the UK’s decision to leave the EU “seems clear”.

Le Monde noted that the French figure was relatively low compared with the total number of Britons living in France, which is estimated at between 150,000 and 400,000. But the paper said it showed how worried they were.

While no national figures have been released for this year, Le Monde said numbers from district prefectures suggested the surge in citizenship applications from British nationals would continue.

Ille-et-Vilaine, which deals with citizenship applications for Brittany, told the paper it had received 110 in the first five months of this year, against 50 in the second half of last year. Before the Brexit referendum it received between 10 and 20 a year.

Other prefectures around France reported a similar trend, it said. One spokesperson said most applicants explained at interview that they had “serious concerns about being able to continue living in France” after Brexit.

French citizenship applications can take at least 18 months to process, which explains why the number of people who were actually granted French nationality in 2016 rose less sharply, from 320 to 439, the paper said.