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