Doesn't the school have any kind of ID card? Presumably all the over-15s at the school have the same problem. If they don't have a card then maybe the student council or similar should encourage them to get one.
My 17 year old DS has a NUS student union discount card which does the ID job and gives discounts at lots of places. I think it cost about £10 but has repaid that in pizza hut discounts. They do send it to school or college though. I guess this is a way to prove they are a student. I am sure the school / college will be well used to the process.
Students in 6th form can get a NUS card. DD1 did this. DD2 and DD3 went to college and everywhere eexcepted their College ID Card. They have just changed the bus fayres here, so that 16 to 18 year olds now pay child fayres,