Hi Sylvia,
I'm afraid none of the pickings are especially helpful. Here is what we have:
Thomas Harding abt 1845 Bristol; St Philips Head Bedminster Somerset (this guy is married to 23 year old Mary Ann, son is 3 year old Thomas George. Thomas is a 'fireman of steamer')

Thomas Harding abt 1838 Berkley, Somerset, England Head Compton Dando Somerset

Thomas Harding abt 1847 Frome, Somerset, England Head Frome Somerset

Thomas Harding abt 1846 Bridgewater, Somerset, England Son St Mary Somerset

Thomas J Harding abt 1841 Kilmersdon, Somerset, England Head Cloford Somerset (this guy was listed in the 1861, so I don't think it's him)

Changing the parameters a bit:
Thomas Harding abt 1838 Berkley, Somerset, England Head Compton Dando Somerset

Thomas Harding abt 1847 Frome, Somerset, England Head Frome Somerset

Thomas Harding abt 1846 Bridgewater, Somerset, England Son St Mary Somerset

Thomas Harding abt 1840 Bridgewater, Somerset, England Head St Philip and St Jacob Gloucestershire (this guy is married to 29 year old Sarah, and has two children - Alfred H is 6, Kate is 1.

Thomas E Harding abt 1837 West Cranmore, Somerset, England Head Wapley and Codrington Gloucestershire

Thomas J Harding abt 1841 Kilmersdon, Somerset, England Head Cloford Somerset

What else do we know about your Thomas?