Middle Eastern places are often BYO too. I happen to have two about five minutes’ walk from where I live - no corkage either, and good value food.
I don’t believe restaurant wine prices of 3 and 4 time retail are anything to do with the high costs of running a restaurant. It is how they choose to mark up wine relative to food. It would be difficult for an individual restaurant to break ranks on that, as they would suddenly have a much more expensive (food) menu, and that is what we Brits generally look at when deciding where to eat. But it can be done differently.
Incidentally, @Leah, I would love to know where you can get this natural Sicilian white online for £3.20. My guess would be from Italy - and without paying UK duty, as if you subtract UK VAT and duty, there is about 45p left for everything else. Nevertheless, I might like to put in an order