Come to New Zealand! The NZ bakery/cafe[teria]/"tea rooms" is what you describe; grab a tray and a couple of small plates and go down the side of the establishm

Come to New Zealand! The NZ bakery/cafe[teria]/"tea rooms" is what you describe; grab a tray and a couple of small plates and go down the side of the establishment to self-serve from the hot cabinets with (savoury) pies, sausage rolls, chicken drumsticks and chips (fries); many pre-made sandwiches; and various cakes and sweets. Most have a menu with a few simple made-to-order things as well, e.g. toasted sandwiches. Generally cheap, reasonable quality and a staple of all walks of life over lunch.