Hello John,
The baptism for Ann on IGI only gives father William, not her mother's name
however in the same batch number there is a baptism for a John Wilkinson,
Born 1 Jul 1789      bapt 20 Sep 1789      St Andrew Par Reg And Nonconf, Newcastle Upon Tyne, Northumberland  (same place as Ann)
parents William WILKINSON  and Isabella
What makes you think William and Isabella married at Whitburn?
IGI has a possible marriage for the above parents
William WILKINSON  to  Isable THOMPSON     
   2 Feb 1772   Saint Andrew, Newcastle Upon Tyne, Northumberland    
You may be able to find more information on the free site looking through the bishops' transcripts:
http://www.rootschat.com/links/05mf/Barbara