I hadn't really heard many good comments about Pulse (vegetarian resturant) in Norwich, but I went in there today and was quite impressed. Lunches are generally around a fiver per head (maybe more if you have a more expensive drink) and most things can be veganisied. I had the Mexican panini - you have to ask for the vegan option for this. It kept my blood sugar reasonable for the last couple of shops and the journey home, and my (omni) mother liked it.
Edited to add: for more information about eating out as a vegan in Norfolk, see the VegFolk guide.
Essex (I haven't spent as much time in Essex so don't know how useful this is, but the site looks good)
Cambridge (My favourite of the cafes on here is CB2. They have another branch called CB1, on Mill Road, which is not listed but you can certainly get soy milk there. And books.)