I understand that on the days she receives the Prime Minister she carries a brick in it, so she can take a swing at him if he becomes too insufferable, as the one the character in Fings Ain't Wot They Used T'be, by Lionel Bart, carried "for awkward customers".
As women's clothes are still made without serviceable pockets I imagine HM had a packet of kleenex or a hankie in her handbag.
Probably a powder compact as well - I don't remember seeing her with a shiny nose, do you?
There may not be anything in it, of course - when she was young all grown-up ladies had handbags and most of them clung to them all their lives. HM is probably doing the same.
If she's reading this I hope she enjoys it and has a good laugh. Although I would advise her not to read any of the Andrew or H&M threads definitely! It won't be good for her health.