Odd one! In 1851 he gave his birthplace as Hatley, Beds (not Cambs as you were told previously). So that's Cockayne Hatley as the other two Hatleys are across the county boundary in Cambs. All three parishes have been extracted onto the IGI but there's not a single Giddin(g)(s) baptism in any of them.
Banns for his marriage to Mary Wagstaff were called in Biggleswade on 1 Apr 1798, Robert Gidings of Sutton and Mary Wagstaf of Biggleswade
Sutton has also been extracted onto the IGI but there wasn't a Giddings baptism for over 150 years before the wedding.
So where was he from? Somewhere in the locality I'm sure.
The NBI shows no burials in either Sutton or Cockayne Hatley that could be Robert's parents (no Giddings at all in CH). The only places in that part of Beds where there were Giddings burials were Potton, the last being in 1777, and Eaton Socon. I think he may have been from Potton, but that's just a guess and without a baptism is unprovable.
Like you, I can't see an obvious baptism for Mary Wagstaff either. It might be a case of having to go through all the baptisms on the IGI in that part of Beds, and try to tie them up with burials and marriages
I've checked the Muster lists, A2A and Blars online catalogues and drawn a blank.
I'm stumped!
David