Just spent 2 weeks in Ireland and Scotland, we were only denied once asking for a take away box over about 6 times we wanted it. Half the time the restaurant boxed it up for us. Even a 1* in Edinburgh had no issues packing up our petit fours in a little box for us but no bag provided.
Edit: Just remembered one seafood place was a bit of a bother. For one cream pasta dish tried to give us the same flimsy compostable box that the other two dry dishes we had and they had to go look in the kitchen for a plastic container. We also had to acknowledge that restaurant had no responsibility for the food once if their their establishment.