This is so interesting, thank you! I wonder if it can be the same person - looks like a trip to the BL may be in order.

I paid for the full article in the newspaper archives. The text is:

'Although she doesn't know a note of music, Mrs A. M. Booth of the Old Queen Anne Inn in Hucklow, Derbyshire, has had five songs published by a London firm of music publishers. She is writing a new song, entitled "Some Day".'

It makes sense there might be a co-writer of the score, therefore, if she couldn't write music. And it might also make sense that her initials were used to keep her more anonymous.

I couldn't find anything in the 1939 census but I may not be searching in the right way!

Thanks for your help!