Hello Annie, thanks for your reply.
My greatgrandfather's birth cert shows him as Philip William Small born on 26th Oct 1870 at 13 Bermuda St Mile End. Father Philip Small, occupation painter. Mother Rebecca Bethell. His christening record, 20th Nov 1970 at St Thomas Stepney, shows parents as Philip and Rebecca Small, abode Stepney, father's occupation painter. I have found nothing to say that Philip and Rebecca were ever married.
It now starts to get complicated. Rebecca married Edward Edwards on 26th Dec 1876 at St Lukes Holborn, she is described as a widow. From then onwards my greatgrandfather was called William Edwards. His marriage cert shows that his father is Edward Edwards. The story that was passed down to me via my late father and grandfather was that my greatgrandfather knew that Edward Edwards was not his father, but he accepted him as such, and it was something the family never talked about. My greatgrandfather could not remember having a father when he was a small child, his only early memories were of his mother Rebecca and her sister.
What I have done is find everyone I can called Philip Small in various records. After a process of elimination I am left with only one possibility who is Philip Small born around 1844 in Dundee. I have located all his census entries where he is showing as a painter or scenic artist. He married Elizabeth Maddocks in Belper in 1873. He died in Paddington on 4th May 1931 aged 86 years.
So as you see I have no proof at all so far. It is just that this Philip Small from Dundee is the right age and occupation and seems to be the only candidate left after looking into everyone else I could find with that name. I'm still in the process of swapping documents with the people I have found who are descended from this Philip Small and his wife Elizabeth Maddocks. Fingers crossed there may be some clue there.