James
Welcome to gods country!! or should I say county!
Depending which end of the county your moving to your best bet will either be Carlisle or Walney(Barrow in Furness).Theres a couple of firms offering hire at Carlisle.Border Air Training or Carlisle Flight Training.You can find a fair bit by turning up in the Cafe(Under Tower) around Lunch Time where most of the Instructors will be dining.You can find out more of course be checking their website's.
BAT Home page
Carlisle Flight Training - Flying Lessons Cumbria - Welcome
Sorry Cant vouch for Walney as Ive not been in there.
Cheers