I have rarely seen an American King sized bed in a UK hotel. Double means one bed for two people, usually a double or maybe queen sized bed. Twin room will almost always be two twin beds (also called single beds). A single room can be one twin bed meant for one person, you might get lucky and get a double bed or two twin beds, but there are no guarantees.

This is why you have to be careful with the Hilton Honors spouse stays free in countries outside North America. Booking a room for more than one person usually costs more than a one person price. For Hilton, you book a single room at a single person price. Then you have to make sure and contact the hotel or Hilton Honors so they know there will be two people and thus needing a bigger room per the terms of the program. Failure to get this noticed prior to showing up at the hotel could cause problems and you potentially could get a room with one twin bed.

That's also why you don't assume there will always be two double beds that will accommodate parents and kids in the same room for a lower price.