Easiest access on the Avon for decent roach fishing on BAA waters is probably Marlcliff and Cleeve Prior, nice steady water with car parks on the river bank.
An alternative to BAA is Leamington AA's Lido stretch just above Stratford which I think is available on day ticket. There's a large car park just off the Warwick road right on the river bank. This is an excellent area for roach on maggot or seed baits and is fishing well at the moment. I had 25lb+ weights while staying at the cottages just upstream of here a couple of weeks ago and would probably have caught more if pike hadn't shown up.
Bbest on the Severn heading into autumn is Ladyham or Ribbesford.
Ladyham has parking on the river bank and is a decent stretch.
Ribbesford has roadside parking in lay-bys along the top (shallower, about 3' at normal level, stretch) or you can park by the football ground for the bottom end where the river deepens considerably and is good heading further into winter when there's likely to be extra water on.
Further down river Severn Stoke is another good stretch with parking near some of the pegs. This is a deep stretch which requires familiarity with that style of fishing but there's big roach and bream about, as well as the barbel.
