Hi there!
1st time poster (but regular lurker) here! Saw your message and wanted to reply because we live in Finchley. I have a 12 year old DS who has just finished his first year at the boy's comp. over the road from BD.
Secondary school provision for girls really sucks in Barnet. Many of DS's girl classmates from primary school had problems finding a good place, but I would go for the the new Wren Academy like a shot if I were in your situation.
The Compton is impossible unless you live right on the doorstep, and TBH, in spite of great Ofsteds and league table positions, we have seen and heard things about behaviour there which are not so good. Several of DS's friends' parents chose DS's school for this reason.
Unless your DD is VERY academically able, AND you are practising Catholics, St Michael's Grammar will not be an option for her.
BD has certainly had problems in the past, but seems to be improving. You might also consider Friern Barnet school in North Finchley. Exam esults have been poor for years, but there is a new Head now, and I know several parents who are very happy with the school.
Forget about the uniform - all kids hate uniforms - that's the whole point of them!
HTH and good luck!