My geography's terrible so these might be no use to you at all but (don't know if any of them do flyball) there are definitely agility clubs in Cumbria:
Barrow in Furness DTC (I think they have 2 venues, one at Barrow & another at Dalton)
West Lakeland DTC (think they train near Millom/Bootle)
Wigton DTC (think they train near Carlisle)
Dark destroyer agility at Alston but I don't know if that's a club or if Nigel just trains on courses etc. worth an ask though.
If you're willing to go a bit further south there's also Lune Valley DTC or Hest Bank Kennels in the Lancaster area.
They're all places which turn out very good dogs & the people I know from them are nice folk too. I think they all have websites or look on Agilitynet for more details, or even ask on the Agility Forum.