Many thanks Amondg for your replies. Yes, he had an older brother also William George Richardson who was born and died 1839 in Plymouth. I did not know about his sister Maria born 1843 Plymouth and died there age 0 in 1844. Maria's GRO birth record lists her mother's maiden name as Bunker, which confirms the link. Maria's baptism and burial records on Family Search both give her address as Cambridge Street which matches the 1841 census for her parents and siblings.
On GRO, I also found an older sister also Maria who died age 2 in 1838. Her burial record on Family Search also gives her address as Cambridge Street, so that ties in. I have not found her baptism.
Unfortunately, I do not have William George Richardson born 1841's birth certificate. I have not found his baptismal record that might also have included his date of birth.
Thank you for suggesting the National Archives file, which I have now looked at. It would not surprise me if living in Plymouth he had joined the navy. His father had been a long-term soldier.