ex Lancaster J reg's are used for schools in Carlisle area.
as K768DAO said, most school work in the area is done by local coach hire companies, and stagecoach run the odd school service (33C and 33D i think usually come to sixth form). the odd B10m does come occasionally (this academic year, i've only seen one, which was on last day of term, and it carried no passengers!). students will occasionally use the public services if they don't feel like being squashed on a school bus (service 31 in both directions is usually used).
i think the stagecoach school services generally run in addition to the 31 (frizington), and the coach hire companies generally run the services which aren't covered by the service buses going near the school (with exception of workington and maryport, as the stagecoach services running near the school didnt go out that far prior to april 2008.)
i apologise if that doesn't make sense. as usual, i have something in my head that i struggle getting onto computer!