I recently used the LHR Hilton for the day when I was waiting for my connection to PRG. I can attest that I personally slept at the Hilton. The walk is not that long maybe five minutes. Was given lounge access on the day rate as a diamond, didn't go. Shower, nap, then lunch downstairs, and then back to the terminal via LHR express (terminal 4 to terminal 1, for free) to checkin for flight to PRG.
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dallasflyer