Hi
It would be best to check with the School, they will be the owners of the property and no doubt will have a blanket smoking ban to all their buildings and grounds, It would also be useful to ask for a copy of the tenancy agreement to see if there is anything about smoking?.
I used to work for a local authority and this was the case, the caretaker had to leave the premises to have a smoke and had to go to the rear of his property as the front was school facing.
The building was also included as part of the fire risk assessment as it was classed as a commercial property and part of the school portfolio, for example the building was covered under the council insurance policy but not the personal contents as they belonged to the caretaker. In short the school are providing the building as part of their work.
In terms of Legislation I would say FSO.
Regards
Jason