Thank you all for your interest and help with this. I am very grateful.
All the information I have is from my FIL.
He had originally asked for his adoption records from the Nottingham office but he was told that these records had been destroyed in a fire?? He then went on to ask a family member also interested in this side of the family and doing some research & another genealogist from a company if they could find out more information.
The following is from this gathered information.
Given the DNA match to a Henry Albert Goode and address of Beech Avenue, Nottingham - a guess was made that this Mary Parkin was/is his mother - Mary Grundy.
There was a William Arthur Grundy
Dec 12 1885
May 20 1954
and
Sarah Jane Grundy (born Alford/Halford)
Jan 7 1887
May 18 1945
Who lived almost opposite H A Goode & Leah Goode at Beech Avenue
It is thought that perhaps Mary Parkin/Goode had a illigetimate child from this part of the Grundy family and named herself as Grundy on his birth certificate to point towards the 'father' of her child - my FIL. Hence her name on his birth certificate not being her actual name.
We have looked for a Mary Grundy who could possibly be his mother everywhere but to no avail.
It is almost like she doesn't exist & perhaps she doesn't under that name.