"Keep Calm and Carry On" was a promotional poster produced by the British government in 1939. They were only intended for use in the case of a foreign invasion. It was intended to be the third poster in a series of 3, but the backlash against the first poster was so intense that the entire series was scrapped.
In England, copyright law states that any materials created by the Crown lose their copyright protected status after 50 years, so the slogan and the image logo are now public domain (meaning anyone can create products with them).
The British, to my experience, do have the ability to not let what goes on around them to affect their sense of order and dignity. For example a few years ago there were a few terrorist bombings in London, I think, and I watched some of the interviews at the time on the BBC and the general attitude of the Londoners seemed to be "life goes on".