How old are you? If you want you could look at uni clubs.
Plenty of the students paddle mid week. You could get in contact with Durham or Newcastle as both have active clubs. Durham allows non university members certainly.
There are clubs that do pool sessions on week nights. You could learn the basics there. Prudhoe used to be on a Friday IIRC. Hexham also paddle midweek.
Look into canoe polo. It is good for teaching the basics and building the right muscles and control. Again mainly played midweek and evenings. Back in the day there was a very active NE league played in Darlington/Tynemouth and Newton Aycliffe.
There is also the Teesside barrage - not sure if there is a club there but it is sort of flood lit or at least it was and I used to spend many an evening surfing happy eater.
If you are small my wife is selling a I3 221 Sadly my boat was sold years ago and I haven't done any proper paddling since 2008. Still occasionally dabble in a bit of open boating and sea kayaking for holidays and trips. Didn't have the motivation to keep up the whitewater stuff. Too hard to get competent people together when the rivers were up and the local clubs seemed to be aimed at kids and beginners rather than people wanting to paddle purely for fun on 3/4 type stuff.