If you’re newly arrived in Luxembourg you’ll need to register with your local commune (council).
If you’ve been here for 5 years or more you should consider applying for permanent residence and the right to vote in local, and European Parliament elections.
You can also apply for Luxembourgish citizenship. If you’ve lived outside the UK for less than 15 years you are still entitled to vote in UK general elections and referenda (provided you have registered to vote in the UK (double check)).
There’s a lot of information available on all aspects of life in Luxembourg (including for people who have yet to move here) in our sections on residency, citizenship and voting.
List of medical facilities/practitioners in Luxembourg (Prepared by British Embassy in Luxembourg)