The office I described on the A4 at Cranford, Heathrow House, was a nightmare to get taxis to from a Heathrow terminal, where they had been ranked up for an hour or two anticipating a job to The City at least. It was next door to another hotel, the Berkeley Arms, which has also been demolished and a Doubletree built on the site. But if you asked the taxi driver for the hotel instead, which didn't have its own shuttle bus, they knew they could be given a ticket by the doorman which allowed them back to the head of the taxi queue at the airport. Driver still grumbled though.
Probably early 1980s, when standby transatlantic tickets had their time, the company there, based in Detroit, had a miserly US managing director Mr X who wrote around that travel to the US, which there was quite a lot of, should henceforth be by standby, "as it's cheapest and in my experience there are always seats". What a pain to have to go to the airport twice, once when the ticket office opened and once for the afternoon flight. Said MD was also provided with a Daimler and chauffeur - the classic sort of such driver, had the job for years and seen all the top management come and go. One morning the manager of the Newcastle office had come down on the first BA domestic to a meeting, and was walking out of Terminal 1 when he sees said chauffeur standing in the ticket counter queue. So he goes up to him. "Hello, what are you dong here". "Oh, Mr X is going to Detroit this afternoon so I've to come over for his standby ticket. Hang on a minute and I'll give you a lift back to the office ".
It's surprising that over the decades Heathrow never sorted out short distance taxi journeys from the terminals.