I recommend getting the marriage index for Oxfordshire as this will help with marriages pre-1837 in the county.
A William GARDNER married an Alice WARD in Hanwell 4 October 1730. He is noted as coming from Deddington.
Clifton is a apparently a hamlet of Deddington so if you have that CD you have Clifton.
William GARDNER in 1714/15 son to Richard and Mary could very well be the one marrying Alice. If he survived. They did marry young in those days, so I'd keep him in mind.
Hanwell is on the Banbury CD no.3 unfortunately there are only two WARD entries and one is an Alis who was baptised in 1704 to John/Elinor.
There are GARDINERS in this parish too but I couldn't see a William around Alice's birth. If this is our Alice I do have my doubts about the 1715 William