There is no especial genetic link between Galicia and the British Isles, I believe that is between the British Isles and the Basques. There is a general link between the Isles and the western coast of Europe as would be expected.
The term Celtic, other than in the last couple of decades has always had a language component attached to it. The Boston Celtics is sort of an exception. They are named for an earlier team from New York called the Celtics and were named at a time when Boston was filled with Irish. The obvious Irish team named Celtic was the original Celtic FC in Glasgow which was founded by Irish immigrants who in the late 19th century would have still been Celtic speakers.
Incidentally, Henry McCarty aka Billy the Kid, spoke Irish as he was born into an Irish community in New York where the language was still strong and where the Celtic name for later basketball teams came from.