Just for info, Melvyn's name is misspelled in the GRO index (I checked the image at Ancestry): GAUGH.
You could add a correction/note to the index at Ancestry (you can include his full middle name and correct surname in the entry, and add notes to give other info), so that anyone else who searches for his birth can find it. When I do that, I include a permanent anonymous online email address in the form
nickname at gmail dot com
so that messages will always reach me. I have had several very useful contacts with distant unknown family members via corrections/notes added to censuses and other records there.
FreeBMD doesn't seem to have transcribed the birth yet but when it does, it will have the incorrect spelling, of course. You can't correct records there if the information is accurately transcribed from the GRO index, but you can add postems -- you could do that on any record, including RMG's birth, etc. Since there is no PM system there, you need to include an email address if you want to be reachable.
Not everybody bothers with trees at Ancestry - it's good to make one's self visible right on the records themselves.

There is no entry on line at Last Post (Canadian Legion, veterans' death notices that come to their attention) for RM Gough.
EDITED to remove full name of father of Melvyn since later posts show that there is a possibility he is living -- I trust that all others in this thread (including the author of the OP) will do the same!