I don't think it's cheapness, I truly believe it's just not part of their custom. Gambling is another thing that the British are not fond of. We sailed on the Sea Princess after she had returned from P&O. They had removed half of the casino and turned it into an area for board games and cards (bridge, gin, and the like).
Corkgirl, you are so right. Not all Americans do tip. Usually the ones that can afford it the most, tip the least or not at all. I know from waiting on a few "stars".