The Free BMD project shows William Thornton marrying Mary Killip in Birkenhead in the March quarter of 1866 GRO ref Vol 8a page 558.
A copy of the marriage certificate can be ordered from the GRO (http://www.statistics.gov.uk/nsbase/registration/FRC/frc_certificate_obtain.asp) or more cheaply from Cheshire County Council (http://www.cheshirebmd.org.uk). Although this marriage does not yet appear on the Cheshire BMD index so be careful as there are other marriages involving people called Mary Killip or William Thornton around 1866 in Birkenhead.
I can't help you at the moment as there are a number of possible Mary Killips in the Liverpool/Wirral areas at this time - I need more info such as age at marriage and father's name. When you find out more about Mary from the marriage certificate, I might be able to be of further help - try e-mailing me direct at firstname.lastname@example.org with the marriage certificate info.