Hi everyone! I'm not sure how to mark this enquiry "solved" but it is! I've found Gertrude!
Many of you on here have helped me so much and I'm so grateful, the least I can do is update you on my progress!
After a fair amount of research, I found out that Gertrude moved to Jersey in 1945. She met her "husband" [although I still can't find their marriage certificate yet] Harold Arthur Goldsmith and they moved to Jersey, where Harold was from, along with Gertrude's first born daughter Joan Isabel. They adopted a two day old baby boy in 1945 in Guilford just before the move. I wonder whether this was related to any guilt that Gertrude might have felt at giving away my dad at birth??
I've spoken to Gertrude's adopted son on the phone and he was really friendly and kind. Told me lots of information and he's going to send me a photograph of my grandma.
Gertrude died age 47 in Brompton Hospital in London in 1954. Apparently she was ill while on Jersey and went to Brompton to get treatment and died there. She is buried in a common grave in Brompton Cemetery.
I would still be interested to know where Gertrude was between 1930 (in Edinburgh) and 1945 (in Jersey). She and Harold had a brief spell in Milford Haven, Pembrokeshire in 1945 but I have no idea where she was before that! Scratching my head as to what brought her so far down south. But this helps explain why her Auntie Isabella died in Jersey in 1947. She was obviously down there visiting.
Also Gertrude's daughter Joan returned to Aberdeen to give birth to her daughter J ***** in 1949 so there is obviously still some connection to Aberdeen.
I just wanted to say thanks SO much everyone here on Rootschat for all your input and help, especially @hgs46
I can't actually believe that I have found her!!