Tony
I have never seen the birth certificate (1893 Banbury I think). The Ethel was, it seems to me, to be the one mentioned in the 1901 census living in Hook Norton and in 1911 she was a housemaid in Castle Bromwich. The only likely William Sulley I can find is living in Hinckley in the 1911 census.
What I cannot understand is how Ethel ended up getting her child adopted in Nuneaton. I assume she must have known the Hammonds before the adoption but where and how I cannot think.
I assume you have already found the census entries on Ancestry but if you cannot find I can send you images.
See

http://www.coventrytelegraph.net/news/coventry-news/war-deat...

This chap was (is?) a reporter on the Telegraph and is descended from the family - he may be able to help further.
Richard