Hi Myfi,
The parish register for St. Mary of Charity at Faversham does provide the same detail as provided in the IGI, namely:
Mary Martha WRIGHT chr. 18 Dec 1815 to parents John and Martha WRIGHT.
There are no other children christened to this same couple at Faversham and neither is there a marriage of a John WRIGHTto a Martha at Faversham.
However, there is one other child christened at Faversham to a William and Martha WRIGHT - Harriet WRIGHT on 25 Dec 1814.
There is also a marriage of a William WRIGHT to a Martha SMITH at Faversham on 19 Mar 1814, he a bachelor, she a spinster, both of this parish by banns. Wit: Sarah Douglas, George Hunt.
There was a Martha Mary SMITH christened at Faversham on 11 Dec 1785 to parents John and Mary SMITH but there are too many John SMITH/Mary marriages to pin down which couple were her parents, without more in-depth research.
There is also a burial of a Martha WRIGHT at Faversham on 22 Mar 1835 aged 48 [born circa 1787] making her of the right age to have been married during 1814.
There is no John or William WRIGHT christened at Faversham at any time but there are some christenings of each at Ashford, Eastwell, Charing and Little Chart.
I hope some of this helps gets you started, though.
Good luck.
Sincerely,
Susan