Nicola, doesn't your husband know his mum's name? It will be on his birth certificate. If he doesn't know it and doesn't have the long form certificate, he should get a copy.
With her name, a search can be done for her birth, whether she married, and her death.
Her birth certificate will give her exact date of birth and her parents' names.
If she married, her marriage certificate will name her father, if she gave his name.
Her death certificate might be signed by a husband or partner, or a child.
She would have been born by 1911, so she could be found in the 1911 census with her family, hopefully, and that would tell you about any brothers and sisters she had.
Also, the 1939 register is now available to be searched on line. If his mother was still living in 1939, she will be on it, and it might show that she was living with a husband or partner. That would also confirm her birthdate, for example.
For info, John is shown in the 1939 register at:
Central Home For Children Hartley Road, Nottingham
I don't see the other children; they would only be shown there if their deaths have been added to their entries since they were under 18 in 1939.
You can put her name here since she is deceased and it is her parents and so on that you are wanting to know about.
Since your husband's father was not named on his birth certificate, there is probably little he can do to learn his identity, if his mother never told him. (You haven't said whether he knew his mother when he was older.) If he was adopted, his adoption file might possibly have information.
There is a possibility that YDNA testing - the DNA that is passed on from father to son to grandson etc. - might find him a match that was close enough to investigate whether the match's surname is a possibility. At this point, so few people in general have done DNA testing that the chance of a match is very low, but it's always something to consider.
Best to start with his mum's info and work on tracing her side of his family.
And also not to wait 2.5 years to acknowledge replies.