I also dislike 'Lady' Doctor, because my grandparents use that term and also fully reject the idea that men and women do the same medical training. To them, the 'lady' doctor is a less qualified doctor.
In reference to Mrs. Thatcher- 'Female' is correct to my ears.
I think that "female" sounds better in this context, but there is nothing wrong grammatically with using "woman." In English, nouns are used as adjectives all the time; its just that man is not commonly one of them.