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Good afternoon, thank you for contacting Just Answer my name is***** am a solicitor and I will be assisting you today. The title documents should confirm whether the wall is a party wall, however this may not always be the case, if the title documents are silent it would be presumed to be a party wall unless one party could prove otherwise.
The title documents should be available to download from the land registry on the following link: https://eservices.landregistry.gov.uk/eservices/FindAProperty/view/QuickEnquiryInit.do
Please note that a call requires a further fee, if you would like a call I will be happy to arrange one with you.
The school may not require planning permission, however if the wall is a party wall then they will be required to serve you notice under the Party Walls Act 1996, which requires you to be given at least two months notice before the work is commenced.
In the first instance I would discuss the matter with the school, (however time is off the essence) if this is not then resolved I would then contact the planning department to object.
Glad to be off assistance, I wish you all the best going forwards.