I've only just found your post!
I have been looking for the WHITING family from SHEPTON MALLET, SOMERSET for some time, and was wondering if they might have something to do with your Bristol WHITINGS.
HENRY WHITING B. 1822 moved to Wrexham, N.Wales by 1861, married ELIZABETH (nee?)and then moved with his family to London.
I can find no birth or census entries for him in Somerset, therefore have no idea who his parents were.
Hoping you might be able to help.