Hello Sue
As you've discovered there aren't any Trimmers anywhere in Warks.I've checked the NBI which is a good indication & there aren't any burials in that name either.
The name appears to be from the home counties particularly Hampshire.
The possibilites are that she was born in B'ham to travellers,boat people etc. & christened elsewhere or not at all,she was christened in a non-conformist chapel not listed by IGI,she was born elsewhere but spent much of her life in B'ham,she was married before & Trimmer was her previous name or her parents were from Europe & the name has been Anglisized.
Not much help I know but you may have to consider these possibilities.
jim