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I believe it's called 'The Million Dollar Door', rather than 'The Millionaires' Door', because, as CWS correctly states, BA paid a significant amount to Heathrow towards the end of T5 development to allow them to put it in. It was somewhat of an afterthought during the building phase, not part of the original plans, when it was decided that something should be done to smooth the journey to the lounge for First Class passengers.

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