Hi,
I am not sure where your family came from.  Is your William Joseph WRANGHAM the one bap 26 Feb 1815 St Clement Danes, Westminster?  Parents: William & Sarah?   I have had a quick look to see if I can find the parents' marriage but seem to have drawn a blank here: any ideas?  Also, I looked at the batch number to see if any other children were baptised to this couple here: none!   They could have moved into the area.   There were a couple of other WRANGHAMs having children in Middlesex at this time: JOseph/ James - I wonder if they are William the elder's brothers?
Sorry I can't give you a firm answer.   You seem to be right in that most WRANGHAMs seem to come from the 'north' - Cumberland and Yorkshire in particular.   If I can help, I will.
Louise