Blimey Smudge, get your OS map out and look for blue squiggly lines!
Yorkshire and N. Wales were my stamping grounds and there is loads to run at. The problem I have is that I would be looking for wild water but you are probably wanting something a little more gentle. Here is a few to get you started...
River Ure, Wensleydale - one or two rapids but nothing over grade 3, except Aysgarth Falls (easily portaged by footpath on true river left) and Redmire Force (portage over rocks on river right)
River Wharfe between Hubberhome and Otley- Mainly flat with a few shingle rapids, but some notable rapids/falls to avoid. Most are easily spotted, but look out for Connistone Falls, Linton Falls and Appletreewick Falls.
River Lune - From Kirby Stephen down should be suitable.
I would suggest you buy this
http://www.amazon.co.uk/Yorkshire-Ri.../dp/1871890160 but it is a bit pricey. I have a copy that is not used, PM me your address and I'll post it out to you.