Re:
Sorry I've come a bit late to this thread. I'm a kayak instructor (and live in North Yorkshire), hopefully can give you some advice.
As was said above British Canoeing membership will give you your waterways licence but always check whether there is an access agreement in place for the waterway you want to kayak.
Lessons are a great idea, you have Hatfield lakes near you too, which I have good reports of
https://www.dclt.co.uk/venues/hatfield- ... ty-centre/
With regards to kayaks, if you are only going to be doing the more placid water aspects of kayaking have you considered an inflatable kayak? I used to be very sniffy about them but in recent years they have come on a lot and we have an itwit 3 from decathlon as a family kayak and it's brilliant, much easier to transport and store than a rigid sit on top kayak. If you do go down that route my advice is to spend good money on sectional paddles as most one's supplied in packages are rubbish.
Kayaking like biking is a brilliantly diverse sport where you can go for a gentle poddle on a river to full on white water/surfing (my passion)
And lastly just a bit of advice on paddling canals, if there are fisherman about give them a wide berth and be respectful. Most fisherman are lovely people but over the years I've had a few run ins with some less savoury characters who believe they have sole rights to the water (a bit like the biker/walker issue), this seems to be more prevalent on local canals.
If I can offer anymore advice just let me know