Joelsnan What has "Auf Wiedersehen Pet" got to do with Eastern Europe? I mentioned it because it involved working lads working in an EU country. Presumably they didn't have villas in France or learn foreign languages at school.
I don't know how many UK citizens in total commute to other EU country. However, I personally know a few.
1 Two small business owners who have manufacturing bases in EU countries.
2 An IT specialist with clients in other EU countries.
3 A friend whose mother is German and lives in Germany, who has now established clients in Germany. (He's still hoping that somehow he can find a way to move to Germany himself.)
4 A specialist in car battery technology, who commutes on a weekly basis to Germany and is just waiting until he can relocate his whole family.
5 Two people who work for big pharmaceutical companies. One commutes regularly to Brussels to pitch for business. The other is a researcher and flies most weeks to Sweden with Astra Zeneca's own airline from Cambridge Airport.
6 A gardener who is currently advising and working on a community city garden in Berlin.
7 An environmental specialist, who regularly visits towns and cities throughout the EU to research how other places manage their waste.
8 Somebody who owns a coach company. Not only does he run tours to EU destinations, but he sometimes goes to visit hotels, restaurants and sightseeing operators.
9 A music critic, who goes to gigs, mainly in Germany and Holland.
10 A medical researcher, based in Cambridge, who spends months during the year working and lecturing in Germany.
11 A restoration expert, who regularly travels to (mainly) northern EU countries to advise on the best kind of glue for various projects.
12 I know somebody who used to work for the European Medical Agency in Canary Wharf before the agency was relocated.
13 A building site project manager, now retired but spent much of his working life in Germany and the former Eastern European countries.
14 A young man, who used to work in the steel industry in the UK, but now works on windfarms in Spain.
15 A number of young teachers who have jobs in international schools in various EU countries.
The above are all people I know personally and there could be some I've missed.
None of them spoke a foreign language fluently before they started, but all of them have made an effort to learn. All it takes is a positive attitude.