Sorry, I'm a bit useless for local information as I only moved here 3 years ago and I'm only just getting to grips with the Leamington/Warwick local area. I joined BAA 3 years ago and still haven't fished any of their waters.
If it's anything like the Avon near me, it will be very slow flowing with some quite deep pools. Ideal for lazy trotting. Plenty of roach, dace, chub (mostly small but with the odd big one), perch the odd barbel but very large and, of course, my favourite, decent bream. Speaking to the occasional barbel fisherman, it appears that they get a fish, on average, every couple of (short, evening) sessions which seems pretty good to me. All baits are good but I've caught my best bream on spicy soss pellet-os
As a small-fish fisherman, I often have trouble with pike killing the swim for half an hour, then they come back and it's on and off all day.
All that is near me though. It may be a different river where you are going. Let us know how it goes.