Have you tried Lancashire OPC ? It is the best resource for Lancashire Parish Records
http://www.lan-opc.org.uk/I have a had a quick look and between 1841 and 1870 there are hundreds of baptisms for a Thomas Haworth/Howorth across the county of Lancashire. Unfortunately it isn't an unusual name in the area.
If he really was born in "Manchester", these are the Parish areas on the site that would be classed as the city.
Ancoats
Ardwick
Blackley
Cheetham
Chorlton-cum-Hardy
Chorlton-on-Medlock
Collyhurst
Crumpsall
Didsbury
Flixton
Gorton
Harpurhey
Heaton Norris
Hulme
Manchester
Miles Platting
Newton Heath
Old Trafford
Rusholme
Stretford
Urmston
Withington
It does seem a coincidence that the two men have the same alias as a surname and are committing the same type of crime. I sympathise with you because we had a swindler, as well as other crimes, in our family tree and she used an alias. She was convicted under her "real" registered birth name but went by, and was mostly convicted under, her mothers maiden surname. The problem is that lying is their trade and so it is hard to know what to believe about any name or age.
I would look for other criminal records and also maybe some other criminals in the family. Maybe he was born Horatio and Thomas was a name he used day to day? I would think he is most likely English/British, as the name was likely inspired by Horatio Nelson. If he had a "Lancashire accent", then the Lancashire OPC is your best bet for Parish Records. It is a great website for anyone researching the county.
Added -
Hadn't noticed the other topic.
This one?
http://www.rootschat.com/forum/index.php?topic=759912.18
Thanks aghadowey