Since I'm freshly back from London, thought I would offer some thoughts on taxis.
It’s England, so taxis are neat and orderly and follow the system. I was concerned about rogue taxis but they all seem to be licensed and legal. The city is just crawling with them, if you want one you can easily get one. Be aware they’re not all black, some are covered in ads or painted but they are all the same shape. If you decide to take one to or from Heathrow, just assume it will cost $100. The taxis are huge inside, not just a bench seat but at least two facing jump seats. So you can easily pack 4 or 5 people into one, unless they have luggage. There is no trunk – the bags ride inside the cab with you.
There are USB charging ports and a credit card terminal. The expectation is that you are going to use a credit card (or Google Pay or Apple Pay) and tap to pay – if you want to use cash you should say something upfront. Sadly the driver is totally encased in plexiglass, with an intercom system to talk with you. So if you were planning on hearing the driver’s life story or his views on politics or religion, or sharing yours, too bad. London busses are the same.
I messed up on my first cab, I had been spending too much time on the France and Italy forums and had the concept of no-tipping drilled into me. So I undertipped in retrospect; I later probably overtipped another cabbie so karmically perhaps I balanced things out. Others can advise but it appears you should tip at least a pound and perhaps 10% on longer rides. Give them as much info as you have to help them out, don’t just say Hilton say Hilton Knightsbridge.
For a major city traffic moves surprisingly well and there are bus and cab lanes they will pop in and out of. Once we got stuck near Buckingham Palace and the guy felt bad that the meter got up to 6 pounds and we hadn’t moved, so he cheerfully reset it and started over.