There was a William Henry Wheatley, a dentist, who worked at 120 Harley St around the turn of the century (he appears at
www.historicaldirectories.org in 1895 and 1899 directories).
http://books.google.com/ shows him (search for "Wheatley, William Henry", as L.D.S. Eng and Glas. at the same address in 1892. Perhaps someone can find him in 1891. I don't think he's the same as William Henry Wheatley the brother of James Charles John Burram Wheatley as by 1881 he's still living with James and Elizabeth and his occupation is joiner.
Perhaps the family got mixed up between two William Henry Wheatleys.
Google Maps streetview allows you to "walk" virtually along Harley St, and there's really no place to have a statue but it could have of course been in a property or somewhere close to Harley Street and not actually in the street itself.
Some work has been done here on the family, who seem to have come from Staffordshire:
http://www.rootschat.com/forum/index.php/topic,424411.0.htmlI do have to wonder how your uncle knew, just from seeing a statue in London, that you were related to this man. Most tales get bigger with the telling. There are references to some very early Wheatley's in London who were surgeons:
http://www.usgennet.org/family/bliss/features/2002/may/pages1419.htm (Richard, barber-surgeon in London, b. 1692)
Even if you do find what might be him you could spend a long time trying to find a connection which may or may not exist. I don't think it's to your advantage to expend a lot of effort in this direction.