I happen to have a loan copy of the Hampshire Genealogical Society Baptism Index 1752 to 1812 at the moment and did a search for you. I could only find one William Frampton born about 1772 in Hampshire: Frampton, William, Parents: Thomas & Mary, Baptised 31 May 1773, Otterbourne Otterbourne is about 4 miles south of the county town of Winchester.
I searched for other children of Thomas & Mary Frampton in Otterbourne parish and found: Elizabeth, Baptised 31 December 1775 Thomas Baptised 3 February 1771
I have a copy of the HGS Marriage Index 1751 - 1812 and looked for a possible marriage of Thomas & Mary. Found one result: 13 February 1769, Frampton Thomas, Ely Mary married in Twyford Parish. The Hampshire Twyford should not be confused with the larger town of the same name in Berkshire. The Hampshire Twyford is a village between Otterbourne and Winchester so this could well be the location for William's parents marriage.
Hope this is of help, please let me know if there is anything else I can do. Regards Ken