HUTCHINS, Watford Area, 19th century
You don't ask a specific question about an individual (which is what the instructions with Ask Chris suggest) and I don't have time to carry out a general trawl over several generations - but I can make a few general observations.
Clearly your Thomas Hutchins (~1804-1846) could not have been on the Victory at the Battle of Trafalgar in 1805 - but the ship was built in 1765 and still exists - on display in Portsmouth. However family traditions often combine an element of truth - with a degree of exaggeration - for instance a sailor in the fleet is often "transferred" to the flagship, and a junior officer ends up as a captain.
You don't state any occupations - and if Thomas Hutchins (~1804-1846) was in military service this might be reflected in his occupation. The address in Watford (which is presumably on the birth certificate you have) may give another clue, and might help you to locate the family in the 1841 census.
I note that a Thomas Hutchins (54, born Watford) was a general labourer living at 33 Sutton Road, Watford, in the 1881 census, with his wife Sarah (53, laundress, born Rickmansworth) and son Joseph (19, general labourer, born Kentish Town, Middlesex) and I assume that this is your Thomas Hutchins junior. This suggests the family was towards the bottom of the income/social scale and may well have been illiterate. Another entry shows a Mark Hutchings (42, army pensioner, born Watford) living at 15 Artillery Place, Woolwich with his wife, and if he is a member of the family it could suggest the family may have military connections.
Finally I should point out that many key records are available worldwide on microfilm and microfiche, and distance does not stop people many people using this site from doing research, at least at the basic family tree level. I live in Hertfordshire but it is far easier for me to get to the Birmingham Records Office by public transport than it is for me to get to see the records at Hertford - which is why I don't do look ups there. Have a look at familysearch and I am sure you will find an LDS Family History Centre near you.
If you can add to the information given above tell me.