Without wishing to sound too smug, it is reassuring to know that my theory was correct. The birth certificate for Andrew WELLER arrived in the post today confirming what I thought was the case, but I was just not quite confident enough to accept without seeing further evidence.
Andrew’s mother is listed as “Mary Weller formerly Newnham”, which is just the answer I was looking for. It is a shame that I had to pay £9.25 for the privilege of getting that one piece of information, it is not as if I really wanted or needed the rest of the information on the certificate, but I suppose now I have his birth certificate I really ought to find out what actually became of him (he is my 4x great-uncle after all).
More importantly this mean I can happily say that my 4x great-grandmother was Mary NEWNHAM and she married Thomas WELLER in Bolney, Sussex on the 31st December 1816. The census records that Mary was from West Grinstead, Sussex, so she is almost certainly the daughter of James and Sarah NEWNHAM of West Grinstead and she was baptised there on the 7th August 1796.
Now I can start work on the NEWNHAM family line with the resources I already have access to, so will hopefully be able to add a couple more generations without too much difficulty.
For anyone who might be interested in the full details from the certificate (and because I have finally worked out how to do tables) here they are: