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"I stayed in that hotel last summer. For some reason they think that £1,600 is an acceptable price for 8 nights in a standard room."

You might have been able to book that same room for less if you had booked it through a different booking channel. That is the reality of hotel booking these days. An "acceptable price" is what the market will bear, which can vary considerably from month to month (or even from day to day). What is the hotel's rate for August, 2016, via Travelzoo?

"I have found a Hilton hotel which I can afford and it says "pay later" I don't know what that means. Does it mean pay at the hotel or wait to a few weeks before?"

"Pay later" typically means that you pay at check-in. By contrast, "Pay now" is an advance-purchase rate which may be non-refundable, or have cancellation penalties.