If the school is in a conservation area the developer can't even repaint the door a different colour (or put up a satellite dish) without council permission, yet alone knock it down!
However there's no
automatic bar to demolishing any listed building, or building in a conservation area. (The Queen can knock down Windsor Castle if she can get permission from the local council and DEFRA!). It's simply that the developer must apply for 'conservation area consent' and the council must use appropriate criteria when deciding whether or not to grant such consent.
As with any form of planning application, local residents have the right to object to the application. (The main difference is that objections to 'ordinary' planning permission are normally only sought, and considered, from those who live very close to the property. If the building is in a conservation area, anyone living in, or around, the whole of that area can object).
http://www.direct.gov.uk/en/HomeAndCommunity/P lanning/PlanningPermission/DG_10026179
Chris