I'm not seeing an Edward Dudley born St. Martin's C.1706.
I can see children of an Edward Dudley born 1720's/30's.
Is it an assumption he was born there as there are children for him.
These appear to be his children:
No mother's name listed.
Thomas Dudley Bapt. 29 Sep 1727
John Dudley Bapt. 13 Dec 1729
Moses Dudley Bapt. 12 Nov 1731
Mary Dudley Bapt. 25 Apr 1735
John Dudley Bapt. 27 Nov 1738
All St. Martin's.
There is a burial for an Alice Dudley Oct. 1741 St. Phillip's.
It states wife of Edward Dudley.