Reading this thread, I remembered I have the autobiography, 'Mandy' (Mandy Rice-Davies with Shirley Flack, published 1980). Miraculously I knew exactly where it was, so I've had a look in there.
Her mother isn't named but there are lots of clues, and it makes you think her mother and father may still have been married to other people at the time.
Here are the relevant paragraphs:
‘The only tangible element of mystery existing in my young life was the reluctance of my parents ever to discuss their past life. How and where they met, how they came to marry, all this was shrouded in secrecy, so that at an early age I deduced, correctly, that each had been married before and that I was not supposed to know.
Mother was born and grew up in Wales. Her father, a professional soldier in the cavalry who never attained a rank higher than private, died young, leaving his widow to raise the family. Mother was the youngest, and rather pampered I suspect. She was very pretty and this led her to the stage. Briefly. Her career ended with a flop, and as job prospects for a girl from her background were restricted, she married at the earliest opportunity, producing a son and daughter in fairly close succession. During the slump of the thirties, her husband believing they stood a better chance of survival by leaving Wales, moved the family to the Midlands where opportunities seemed brighter. It was there she met my father.'
[some paragraphs about her father’s family]
'Daddy had been transferred to the Birmingham police force at the beginning of the war and had met my mother. In old age he has taken to making humourous allusions to their meeting. ‘She seduced me’; but thirty years ago when the memory was still fresh the immediate past was a forbidden topic.
By the time I was born in October 1944, Daddy had been called up as a radio officer in the Eighth Army. He saw his baby daughter Marilyn once before being sent overseas, and I was already a toddler when we met again. My family circle consisted of me; mother; her daughter, my half sister, Margaret who was 16 when I was born and was a second mother to me (my other half brother and sister were never part of our family); and for a brief period, my maternal grandmother, a fierce old lady for whom I felt a healthy disdain.’
So, no definite answers, but a bunch of clues
There's a younger brother David, and after the police, her father worked for Dunlop.
hth
Lisa