"..some are listed as Carroll's and some as Mitchell."
Can you be specific please....how is each birth registered.
"... Carroll, Mitchell Savage and possibly Farmer" Where do you see FARMER?
Census 1911 at 2 Old School Cottage Denton Sussex
SAVAGE Arthur 30y b. West Ham Essex
SAVAGE Harriet 29y b. St Pancras
SAVAGE Harriet 1y b. Brighton
MITCHELL Rose 11y b. Dorking Surrey
MITCHELL Lillie 9y b. Battle Sussex
MITCHELL Bert 6y b. Battle Sussex
MITCHELL Mary 4y b. Newhaven Sussex
GRO birth
SAVAGE, Harriett Hilda mms FARMER
1910 JQ Brighton Vol 02B Page 178
Ancestry Register of births in the Workhouse St Pancras
13 Apr 1881 FARMER female illegitimate mother Harriett