Hi Wendywoo,
I think you're going to have to scour the marriages for a Margaret Ruth Walker after 1933 on the 1837 pay for view site, or in the archives etc , no easy job. And the only way you're going to tell if it's her is if you order all the marriage certs of all likely Margaret Ruth Walker's for the father's ( your mum's granddad that brought your mum up ,and his occupation) name on the cert. Deaths could be anywhere. And like you say you don't know if she got married, and had a different name or was single after 1933, so you do need to know if she got Married or not.
finding a birth for her the same You're just going to have to search around all possible dates from when you think, and all possible years she could have been born. You say your mum was brought up by her grandparents so you should have their names, and they should be on your mum's mum birth cert when you order the right one - could prove expensive if you need to order lots of children named Margaret Ruth Walker birth certs. Maybe you'll be lucky and there is not many of them with a middle name Ruth)
I don't know if you'll have any trouble ordering all the certs from the GRO as the birth is less than 100 yrs old, and if married less than 75. You may be able to order them - don't know.
It could prove very expensive ordering all the certificates if there are a lot of Margaret Ruth Walker's about. I don't envy your task in the least.
Sorry I can't think of an easier soloution
The very best of luck in your search, maybe someone else can think of an easier way, I do hope so
