The baptism records for Brixton parish church exist for 1813 to 1839 so by establishing the father of William you could possibly check the marriage records which exist 1753 to 1837. This still leaves a baptism gap but gives background information.
The Bible Christian movement a form of Methodism was formed a few years after the birth of William so it looks pretty certain that if he was baptised it would have been in a C of E church. The Genuki Devon page gives useful detail http://www.genuki.org.uk/big/eng/DEV/Brixton
It is possible that nearby Yealmpton church was used for a baptism [St Bartholomew, Yealmpton] but unfortunately the records surviving are 1813 to 1840.