I've not visited Yorkshire for paddling purposes (have been to York a few times as a tourist/visiting friends), but if you'd like to paddle with locals you could introduce yourself on the www.SongofthePaddle.co.uk
website and post in their meetup section. Although it is formally an open canoeing site rather than kayaking, it is very friendly and there are loads of people there who do kayaks as well as open canoes. I've taken my folding kayaks to sotp meetups in various places around the country and been made very welcome—occasionally good-natured ribbing about 'bring a proper canoe next time'. Someone will recommend routes you could follow or point you at blogs of paddles in Yorkshire. And I expect someone would be able to put you in touch with local canoe clubs (in UK 'canoe' is used for both kayaks and open canoes).
There is a useful resource for planning journeys on UK rivers and canals called paddlepoints (I forget if it is .net, I think it is; forgive me for not checking). It has a zoom in map which shows get-ins and take-outs, and can also be searched by river name (which I find works better for me) and sometimes has other points of interest (such as places where there is a history of difficulties with fishermen—a few rivers in England and Wales, by no means all, have a low-level dispute about whether or not fishing syndicates can 'own' a river and prevent paddlers' navigation; the consensus among paddlers is that they can not). Canals formally require a licence to navigate on them. In practice whether you'd ever meet someone likely to check a licence is another matter.
Hope that helps. I'm out of the country for much of May or I'd be tempted to try and join you myself, though it's a fair distance from Cambridge where I'm based. (A bit of me is also tempted by your xt-15, though as the owner of several folding kayaks, I hardly need another boat. I think I had better restrain myself ...)
All the best,