There is a 1934 Leeds birth with second name spelled Brian.
Can see, I think, his parents on the 1939, but two redacted entries.
So either not yet deceased or died in another country
So as Darnity said, you will need to get your grandparent’s marriage certificate.
If you are not sure of your grandmother’s previous surname look for your father’s birth in the freebmd indexes.
Hopefully not too common, and only one obvious marriage which you can then order from the GRO to age occupation & father’s name.