I was really hoping that the Kathleen (B) Woolf would have been your grandmother.
I have tried various ways of finding a birth for Kathleen, but sadly can't see anything that fits. Could it be that FreeBMD haven't transcribed it yet? - I don't know.
Couple of things which are puzzling though is you say - "A strange thing though....when Kathleen saw her passport she was surprised to see she was two years younger than she had always thought she was, she had convinced herself so much over the years that what she had told her employer was true!"
I wonder who confirmed her birth date when she had her passport?
When she was in service, surely she would have had to supply a copy of her birth certificate because of her National Insurance contribution!
I'm sorry that there are more questions than answers. It looks very much as though this is a brick wall unless somebody else on the forum has thoughts?
I have at least 3 illegitimate names in my direct line which I will never ever find out the names of the fathers.