I have mad respect for Nigel and I know that the bad "short trip" taxi scenarios he describes do happen. (Disclosure: during my so-called career I became quite familiar with certain airport ground transportation matters. I can assure you that the cab driver's contempt for short trips with their low fares, is universal. If there is life in some galaxy far away, and they have taxi drivers? Those folks will be like that too. I'm sure of it.)
But my experience last November at Paddington was quite positive.
Sadly, on the day I left for London, I was overtired, not ill but I just from a couple of nights of bad sleep. By the time I cleared border control at Heathrow, I was almost scarily exhausted. Worse than my usual "just off an overnight transatlantic flight where I couldn't snatch more than a few winks despite best efforts" condition. I had my cheap advance fare ticket on the Heathrow Express, and had planned to just walk from Paddington Station to my hotel on Bayswater Road, as I'd done before.
Then at Paddington I realized that I was just too tired to deal with that, and frankly I was even a little disoriented and having trouble finding the right exit. So I headed for the taxi rank. There was a man in a safety vest who appeared to be in charge of the queue, which was blessedly short as I walked up. He pointed me into the first available cab in line and even put my 25" checked rollerbag into the vehicle. The cab driver didn't take a crazy long route to my hotel, and even hopped out and unloaded my big bag at the curb. The total fare, including a generous tip, was comfortably under £10.
Happily, I was soon restored to normal with a good night's sleep, and when I left to return home I walked to Paddington with my luggage. (BTW my checked bag is a 25" or 22" roller depending on how much moving around I'll be doing during the trip, and even the bigger bag never comes close to 50 pounds. Unless I'm ill or exhausted I can always manage my own luggage including checked and carry-on bags. By now over the course of several vacations, I have walked several miles along streets, in and out of train stations and airports, etc., with it.)
I think two people with large bags could easily fit into a black cab. A few years ago I shared a London black cab from Paddington to Victoria with another passenger. We both had big checked-size bags plus carryon items and it all fit in just fine. Those fares are regulated by Transport for London. A black cab ride from Paddington to a hotel near Bayswater tube station shouldn't cost a lot.
A question for Nigel and anyone else who knows about this. At my local airport they have a person whose title is "cab starter." They supervise the line of waiting cabs and assign passengers to those cabs in a first-come first-served orderly way, and no a cabbie can't refuse a short ride customer. Am I correct in thinking that the man at the Paddington taxi rank was performing a similar function?