The only place I know of, and a cafe, rather than restaurant - is in Lower Marsh - by day a traditional english breakfast type of cafe and by night they serve (delicious and excellent value for money - i.e. very inexpensive) Thai food. It is a bring your own bottle and it is very popular - get there early.
Unfortunately the name of it escapes me at the moment - heading west it's on the left approx 1/3 of the way down Lower Marsh.
If anyone knows of any byob restaurants though I'd be interested to know about them too.
Agree 100%. Prices very fair, and you can choose to take a few beers or a bottle of something that might really complement the food (I had a good experience with a Gruner Veltliner). The service can occasionally be a bit unfocused, but they're nice people. The takeaway is good, too. No connection etc.