It's not a boarding school, it's an independent school.
They have a boarding house for a select group of pupils (mainly a plot device to explain the pupils who have moved from Rochdale). Most of the school's pupils will live in their own homes.
Boarding schools are schools with a boarding house, some like Eton are boarding only, but others will have day pupils. Both can be described as boarding schools though, even if it isn't compulsory.