As I recall it was "Irish Requests" on Radio Luxembourg. It was either the theme tune or it was played very often.

I used to listen to Radio Eirean too... in Scotland. We even picked it up in Inverness as it was a good steady signal albeit not strong. I used a make shift ariel which consisted of a wire from the garden fence to my bedroom. It picked up the pirate stations too like Caroline and London.

The ariel wasn't needed after dark due to the skywave propogation thingy but it was handy during the day.