Hi,
I am not sure that I can be of very much help, but here is the little I know.
The family of Harffys that I am interested seem to have been apothecaries for several generations, with names like Thomas and William cropping up repeatedly. The surgeon, William Harffy, whose family most directly concerns me, was probably the son of a Thomas Harffy, an apothecary, from Horsham in Sussex whose business was probably continued by his son Thomas Harffy.
Thomas Harffy took apprentice apothecaries in Horsham and in London; I am not clear whether this was the same person who moved (or was simultaneously the proprietor of two businesses) or whether there were two of them. Similarly, Thomas Harffy had children in Horsham whose mother was Mary (whom he may have married in London where another Thomas Harffy was born to Thomas and Mary) followed almost immediately by two children by a woman called Elizabeth (the marriage to whom is mysterious). I am not clear whether these were the same Thomas Harffys or not, or whether Mary and Elizabeth were the same person or not.
The William Harffy that I am most concerned with trained to be a surgeon (a business linked with the apothecary business at the time) and seems to have taken on apprentices in Liphook and Petersfield. His will describes him as living in Portsea (all of which are now in Hampshire), but I can see poll book entries which describe him living in Chichester. He is buried in Chichester Cathedral with his wife.
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=139986541&ref=acomHis wife was plainly a wealthy woman as there are deeds and post-nuptual agreements describing holdings of land around Hampshire and Sussex.
This William has a link to my Blunts, who in turn probably moved to London from Petersfield. (Blunts in Petersfield are mentioned in his Robert Blunt's will.)
So the Harffy family seems to have spread between London, Hampshire and Sussex, including Horsham, Chichester and Petersfield.
My William Harrfy was the son of Thomas and Elizabeth in Horsham (b 1717). Thomas and Mary had a son Thomas Harffy possibly in London in 1712. This Thomas Harrfy, who probably carried on his father's business in Horsham probably married a woman called Mary Turner in London in 1773. (I can see some evidence for this but am relying to an extent on other people's trees that I have not checked.) They may have had children John, William, Mary and Thomas. (Mary at least I can be fairly sure of since she married the William Coleman mentioned in my Robert Blunt's will and is herself mentioned in the will of Petronella Harrfy, my William Harffy's sister, as being her niece, which would fit.) The tree I can see shows the son William Harffy being born to William and Mary on January 19 1745 in Horsham. This is a little odd, as I can't see a birth or christening record for that date, but I can see one for the same details dated 15 July 1743. Neither I nor the other tree I am looking at have anything for him after his birth.
In any event, this William Harffy would have been about the right age to be the one you are looking for, and certainly came from a family with links to Chichester. It isn't a common name, but then again, it could just be a coincidence.
Unless you can find out more about his occupation - an apothecary or surgeon would strongly suggest a family link - then the only other thing that I can suggest is looking at the box that I mentioned before in the West Sussex Archives. If you don't live nearby you can contact them on-line and ask them whether they could copy it for you and how much it would cost.
Best wishes
Alan