That's strange, Rumncoke, as I'm rather similar. I can't read music, but all my Irish side of the family (mother, grandparents and several aunts, all passed away now sadly) were very musical, loved singing, especially funny little songs, and many of them could play the piano. I can play quite a bit by ear including chords, and absolutely love music of many kinds.
I've been playing your Tight Little Island song on Youtube several times and it's stuck in my head now. I was humming it going round the shops!