The process for leaving the EU is specified in Article 50 of the Lisbon Treat.
Basically our government starts the process by giving the EU formal notification of our intention to leave. This is unlikely to happen before the new Prime Minister is in place.
This is followed by negotiations whereby the terms of leaving are agreed between the UK and the EU. A maximum period of 2 years is permitted for completion of the negotiation. If terms are agreed within 2 years the separation takes place. If terms have not been agreed by the end of the 2 years, separation takes place then. There is a clause which permits an extension of the 2 year period if all member states agree.
So, it is unlikely that we will actually leave immediately, but will probably have done so within the next 2 years. This gives the schools plenty of time to decide what they want to do.