Hi OP, what age and profile are you looking for, did you find out anymore on this? I'm also keen to hear more on schools in the area.
Here's what I can tell you from what I've heard:
Feltonfleet: excellent facilities, happy children, not a hot house kind of school (those taking the hot housing type route may consider this to mean less academic but make of it what you will)? Quite big.
Danes Hill: huge school, overwhelmingly I hear of happy parents. Very expensive, a mix of everyone from working families to celebs and sports players. Highly competitive in every sense, especially sports which they excel at. However due to size of school kids have to work really hard to get a place on one of the first or second teams, easy to feel left behind. On the other hand, size of school means there's a club for every interest.
Claremont: parents I know here seem very happy but more widely it has a reputation for not delivering great results academically (not helped by the fact they taught gcse science class the wrong syllabus last year). Reputatkonal concerns over Christian Science links but these seem quite unfounded to most families who are actually at the school? Super location and site, aging facilities but well known for promoting a rounded education
Milbourne: mixed pre-prep and prep, seems to support consistently high academic achievement. I haven't been so couldn't say anymore
Shrewsbury Lodge: very popular mostly boys (but mixed) preprep school, feeds Shrewsbury house in Surbiton (v traditional boys prep). Super early years, nurturing confident and happy kids but you really need to feel that SH is the next step for your son to get the most out of the whole school experience.
Rowan: girls prep and pre-prep in Claygate. Excellent academic standards, good focus on pastoral care, feeds some super schools. If single sex is your preference for girls it's great despite drop off and parking issues.
Have no knowlegde of woodcote, sorry!
HTH??