Well, was she Blanche Mary instead of Mary Blanche by any chance? Did she die in Northampton?
There's this death:
June quarter 1971, Northampton 3b 1458
Blanche Mary Kingston, birth date 27 Sep 1911
Could you tell us the exact phrasing of Doreen's birth cert? Does it say
grandmother for B Clarke/r?
FreeBMD shows several possible Blanche M Clark(e)
For instance:
Blanche M Clark Sep 1911
mother's maiden name: Street
Barnet 3a 865
Did Blanche have siblings? There are other children registered in Barnet with mother named Street: George T in 1913, Olive G in 1918
If you could narrow down the date she married William Kingston, you could purchase her marriage certificate to discover the name of her father.