Thanks again to all who have helped with Gertrude along the way.

I've order Gertrude's birth certificate though Ancestry. I clicked the electronic copy option, but it appears in my confirmation that it will come by snail mail - anticipated arrival Mar 21. Arrgggggggg! That's forever!!!!!

And the cost!
I also sent off an e-mail to Equity - nice little website they have.

So now it's a waiting game - & we red heads are not known for patience.

I will report back when the fog clears.
In the meantime, I agree that it looks quite likely that Christina is Gertrude's mum.
It has occurred to me that Gertrude's birth record appears in the name Ayton while Gertrude in the 1901 census is recorded as "Gertrude Jacob". I wonder if the Jacob surname was a "cover" created after Christina married William Jacob a year after Gertrude's birth.
That may explain why Gertrude never went to London with her parents, instead staying with her grandparents.

The other reason that this popped into my mind is that William Jacob appears to have been from London, so I don't see how he & Christine would have met in the north.
That is, of course, unless that occupation occupation of Commercial Clerk Foils

took him on the road. (By 1901 he was a Translator of course, so if the occupations were something similar it's not out of the question.)
Waiting 5 weeks for arrival of the certificate is going to be painful!