Although I'm a bit too young for WW2, my Mum and Dad served in it, and so I'll try to add what I've learnt from them.Reginald Dixon was the resident organist at Blackpool Tower, and there must be many recordings of his still available, but they might be on organ compilations.
Flannagan and Allen were part of the 'Crazy Gang', and some of their recordings may be under that name.
Vera Lynn was heavily promoted by the newsreels and BBC as the 'Forces' Favourite', but most people (according to my Dad) actually preferred Anne Shelton, who was far more personable.
Les