@ Malfeasance (great handle by the way)
The British "please" is an expression of desire so:
Question, "Would you like tea or coffee?"
Answer, "Tea please!" means "I desire some tea."
This must always be followed up with a "Thank you" when offered the cup, as the provider of the requisite beverage has fulfilled his guests desire.
The Americans with "Coffee thanks" have simply abbreviated this process, and are not impolite, though they are thanking some one for asking a question as opposed to thanking them for the coffee itself (which could be awful or may not actually arrive).