Legal adoption came into being in Engalnd only in 1927. Before that "adoptions" were informal usually - a child was brought up as the offspring of a couple and used their surname or, sometimes, both surnames - his/her birth surname as a middle name.
It was sometimes done that such an adoption was made legal by a donor parent signing the child over to the adoptive parents but there is no register of such documents.
Most such adoptions were of an illegitimate child of a daughter or of a sister so the adoptee was usually a close blood relation. The date you refer to may be significant - his father may have died in the Great War and his mother unable to support him as she would have to find work - perhaps as a live-in servant where no child could accompany her.
You can research a lot on the internet. Obtain a copy of his birth certificate. Find the adoptive parents in censuses - it looks like they would be in the 1901 census. Find their birth details - who were their own brothers and sisters. Many people have great success with such quests.
The mechanisms for all of this will be found on the Beginners Board - how to search for anything of this type.
