I have only ever paid a deposit once, and that was at Chewton Glen, a family-run UK property.

Let's clear this topic up once and for all. Amex don't care what sort of Amex card you use, as long as it is an Amex card - they will get their 3% or so commission anyway! If you want to use a Visa or Mastercard, it is 50/50 in my experience if the staff will let you, since I'm sure Amex can track whether or not the card is used.