Having watched the film last night, I was going to make a post on the music, but you've beat me to it. The film isn't great but the music is very fine, orchestral with concertina as a lead instrument. Looking at the little information there is on the internet, the composer was an accordion player, and (given the whole thing was made on a shoestring budget) I wondered if he played the concertina too ?? Or, as you suggest, it could have been Alf Edwards.
For those unfortunate people who don't have the joys of Talking Pictures TV, I see that there are DVDs of the film available on the internet.