Yes, you do. The Education (School Premises) Regulations 1996 (SI 1996 No 360) specify that every maintained school must have a place where pupils who are unwell during school hours may be cared for and where medical and dental inspections may conducted. The room must be equipped with a washbasin and there should be a toilet reasonably close by.
There are additional requirements for boarding and special schools.
As you are pushed for space, note that the room may be used for other purposes - but not for teaching - provided that it can be ready for use as a medical room whenever it is needed.