Guys - thanks for the debate so far and I have a quick update for you...

The hotel has hit my AMEX with something that approximates to the correct amount. I don't know if they've advised me of the charge as i'm still travelling, but I will obviously be sending them a letter once I'm home querying "the billing to my credit card without my authorisation"

They made a dogs breakfast out of the check-out process, so I feel that some concession ought to be made here...