Welcome to Rootschat, Amanda.
Using Freebmd, it looks as if your mother was born in 1943, so if she is still alive you need to remove her name from your post as Rootschat doesn't allow living people to be mentioned. The same with your grandfather I'm afraid, if you think he is still alive.
If you look at Freebmd
http://www.freebmd.org.uk/ you can find your mother's birth and that will tell you her mother's maiden name. Her birth certificate would give you more information about her parents. There were quite a few births with his name in London, some have middle initials.