Agree with Oundle (for school drama - almost positive that they are not supportive of time out of school for professional work; seem to remember an ex pupil of mine having to turn down a job because it was term time and Oundle said no).
Also:
St Edwards, Oxford - not top flight academic but pretty decent, great theatre, reputation for excellent shows (I've seen some and was impressed) and lots of professional and inspiring staff. Awesome new music centre too, if your daughter is musically inclined.
Uppingham - also a lovely theatre and lots of opportunities. Know less about it though.
Bloxham - small but punches above its weight for Drama, imo. Also not massively academic though.
Schools that I know offer Drama Scholarships (many public schools still don't, or only as part of an all rounder, which tends to suggest they value music and art more highly):
Bradfield (also has a performing arts scholarship)
Bloxham
Bedford (not sure if that's a day school only)
Rugby
Repton
Oundle
St Edwards
Cheltenham College
Tudor Hall
Pipers Corner
Brighton College
However, whether or not any of those schools would have places at 14, I'm not sure (their scholarships are for 11+, 13+ and/or 16+, not 14+)