Good find Janine,

My first thought was that it was just as likely that Sarah was unmarried and John was illegitimate.
Either way - children were often referred to with the surname of their stepfather. Some times they later reverted to their original name and sometimes not. I've examples of both in my family.

However this baptism in Familysearch looks interesting:

John TRIM Christened 31 March 1816 to John TRIM and Sarah, St Philip and St Jacob's, Bristol. batch numbers I04054-6, C04227-5.

So looking good.
If you can find a death of John Trimm snr and maybe get full record of of the marriage to Henry POBJOY which hopefully will say that Sarah was a widow. I don't know whether there is a transcription of those church records but your local LDS centre should be able to get a copy of a film of the original.

Bryan
ps
I see on Ancestry there is a Tree (Truskett Family Tree by mhak124) which has the marriage of Henry POBJOY and Sarah TRIMM. The children shown are Caroline and Thomas both shown as being born in 1826. Those birth dates may be from the 1841 census where dates were rounded down to the nearest "5".
That tree says Henry died 1827 (source www.pobjoy.org.uk ) and Sarah in 1852 so she will be in the 1851 census. Henry's occupation was Tinplate worker. Did someone mention a Brightsmith earlier?