After doing more digging on this family, it seems more likely.
There's a listing for Mary Ann Fryer d. Dec quater 1840 in London, St. Pancras.This would be about right with the birth of Caroline Fryer on the 1851 census.Indeed, there's a listing for Caroline Fryer June quarter 1842 St. Pancras, which matches the date and birth info given on your census.My guess is that the Thomas is the Daniel Thomas Fryer b. abt 1836 in St. Pancras.
In 1861, he shows up in Deptford St Paul, Surrey, Westend:
Daniel Fryer abt 1812Arlingham, Gloucestershire, England Head Caroline Fryer abt 1823London, Middlesex, England Wife Caroline Fryer abt 1844London, Middlesex, England Daughter Daniel Fryer abt 1846London, Middlesex, England SonDeptford Kate E A Fryer abt 1852Arlingham, Gloucestershire, England Daughter Lezzy F Fryer abt 1860London, Middlesex, England Daughter Philip Fryer abt 1850London, Middlesex, England Son
Which makes sense that Kate was born in Arlingham while still living with Betty Fryer.The family shows up again in 1871, in Deptford St. Paul, Surrey.
A Daniel Fryer b. about 1810-1812 in Arlingham doesn't show up after the 1871 census, but there's a GRO death listing, Daniel Fryer, age 70 in December Quarter 1880, in Greenwich, "Greater London Kent London Surrey."Greenwich absorbed Deptford St. Paul, so this appears to fit as well.
So, all the pieces seem to fit together.Many apologies for my dismissing the info.It seems that you have indeed pointed me in the correct direction. : )