I've known the school for the past three years or so and will try and help you if I can..
I would summarise Battersea Harris as 'a school on the up'. It's now in its third year and almost unrecognisable from how it was as Battersea Park. I think initially discipline was very strict, resulting in a significant shedding of both staff and pupils. This has calmed down a bit now, although there is still a fairly tough line on bad behaviour, poorly turned out uniform, homework not done etc. (Although less so than Bolingbroke Academy) These policies seem to have had the desired effect as Harris was listed as one the three state schools in the borough to get 80% passes in maths and English and unlike Ashcroft and Graveney it is entire non selective.
The school is not as green as some but has a sizeable amount of outdoor space and good facilities - pool,auditorium,gym, music studios - it's never going to compete with the private sector but has a lot more onsite facilities than the Bolingbroke Academy. It's very, very diverse in its population as historically it's had places to offer those moving to the borough and many children don't speak English as their first language. This diversity may reduce as the school becomes more 'in demand'. (Harris Greenwich is highly sought after I believe) but at present it seems as if the children rub along pretty well together and the school seems to handle this challenge pretty well judging by its progress 8 score (apparently third in the U.K.)
To conclude, my impressions have been that it's a big, boisterous school with a strong focus on raising aspirations. If your daughter is particularly shy she may find it a little daunting at first but the same could be said about most inner London state secondaries. There is a lot of support for those who want to work hard and improve themselves. My feeling is it will continue to improve year on year.
I hope this helps a bit!