Not a lot of major trout fishing on rivers, I'm afraid, though I have heard reports of the odd one caught on the Arrow and the Stour, and many years ago there were trout in the Avon above Warwick.
The nearest day-ticket river venue is on the Windrush at Burford (about 45 mins - details at the Orvis shop, or join the Burford Angling Club). Otherwise the Warwickshire Fly-Fishers
www.warwickshireflyfishers.co.uk have a project on the river Swift, near Leicestershire, The Cotswold Fly-Fishers have (fairly exclusive) fishing down towards Oxford, and there used to be a syndicate that stocked part of the river Blythe at Packington.
Best bet is westwards to the borders where, apart from the Teme, Usk and Wye etc., the Gamefishers Club
www.gamefishersclub.org.uk have some good fishing.
There's a stillwater near Evesham
www.lencheslakes.co.uk for bread-and-butter fishing, and a sydicate water just north of Stratford. Heathcote
www.heathcotelake.co.uk is near, if you like that sort of thing, Packington
www.packingtonestate.net/fisheries_main.html isn't too far away, and Draycote is definately worth the journey.
I personally drive the two hours to the SDAC rivers near Salisbury
www.salisburydistrictac.co.uk, but the waiting list is currently about eight years.
So, all in all, I'd recommend the Gamefishers.
Regards,
Doc