Ive worked in loads of local authority buildings (youth clubs / centres / of things like adult learning centres, when Ive asked them they usually say there is no ''approved suppliers' list. Schools are the same, never heard of it, facilities guys use who they want, usually ask for copies of insurances and CRB clearance. The only time ive been told I cant work, is then i got asked to do a job at Bluewater, where they wanted a folder if paperwork filled in!
I used to work for a company that looked after all the school kitchens, didnt work in the schools just the kitchens, as this was run by the council not the school.