A long shot here… but, if the programme where the song was played is still on iPlayer, find the programme and find the song. Then, if you have the Shazam app on your phone, use this to find the name of the track, the artist, and links to where you can purchase or hear the track.
I do this quite a lot to find songs I like on Radio Cymru. But, it doesn’t always find the information you want - especially if it’s a new song or the band is unsigned! I have been amazed at what tracks it has found though, so it’s worth a go.
Another way of finding this music is by finding out the artist and using sites like Soundcloud to find the track. Particularly useful if the band is unsigned and using this site to give exposure to their work.
Pob lwc gyda ffeindio dy ganu di!