On the 1939 Register prior to WW11 the name on that register will be his name that he was known by, through his Adopted parents.
He may have been given a different name from the one his mother called him at birth.
My Adopted name was Doreen.
(Name at birth although) I didn't know it when I saw my Medical Card No. was Eleanor Winifred .....
My Medical card No. was FKII 381. So my orginal Birth Record was No. 381 in the Registry book FKII.
All I had to do was find where it was...WHICH I DID AFTER SOME TIME.
However, Now we know the sequence, and with patience. Go through the lists and find the Registry No. and Book - to find THE BIRTH NAME. You mention that you think you know the area and Date of Birth, so it should be a lost faster than the time it took me to locate my mother.
Then I had my journalist friend, fill in the application form (and the Seconded officer, had no idea, The certificate shouldn't have been given at the time!) it took me four hours to locate and speak to my mother after 33 years.
Alternatively, you could go to the Social Services; and as you are not searching for your own parent...and the person for whom you are searching, is a blood line, and long gone...perhaps they will allow you to have your ancestors information.
Failing that.....DON'T BY PAYING ANYONE TO DO THE WORK FOR YOU. DO IT YOURSELF. YOU KNOW WHAT YOU WANT AND WHY. YOU ARE BLOODLINE. APPLY TO THEM DIRECT, ASKING FOR THE INfORMATION. I WANTED MINE FOR MEDICAL REASONS, AND IN 1975 WAS GOING TO HAVE TO GOV THROUGH COURT A LONG DRAWN OUT PROCEDURE AND COSTLY EVEN MY PAYING DIRECT. HOWEVER THE HEAD HONCHO, FOR MENTAL HEALTH, AND I, DID NOT SEE EYE TO EYE, AND HE INFORMED THAT THAT I DIDN'T NEED HIM, I WOULD FIND OUT ON MY OWN (which i did, a few weeks after him, not backing me in my request) BIG PAPER REPORTS AND HEADLINES. I WOULD HAVE LOVED TO HAVE SEEN HIS FACE, KNOWING THAT I DID GET THE INFORMATION WITHOUT HIS HELP, AND BEFORE MY CAMPAIGN FOR ADOPTEES RIGHTS WON THE VOTE IN PARLIAMENT.
AFTER THAT WE ONLY HAD TO GET THE THOMAS CORAM FOUNDATION (FOUNDLINGS) TO AGREE TO HAND OVER THEIR CHARGES NAMES AND CERTIFICATES ----AS THEY WEREN'T UNDER THE ADOPTION LAWS, AND A PRIVATE MEMBERS BILL WAS GOING TO BE TOO COSTLY. WE GOT THEIR RIGHTS TO CERTIFICATES A SHORT TIME LATER. WIN, WIN. NEVER GIVE UP. NEVER GIVE IN. GOOD LUCK IN YOUR QUEST.