Then I actually thought about recent times I've travelled by plane and I realised that competition does exist in London at least. I have:
Spent £50 more (a 70% fare increase) to fly to and from London City Airport. LCY is smaller and as such seems to be much more efficiently run. There's no long walk/shuttle between security and the gate. Security takes all of 5 minutes at most. The check-in desks have no or very short queues and there's seating nearby if you do have to wait. It's closer to the city centre so there's a 20 minute transfer instead of an hour long transfer between the airport and London. This extra expenditure netted me a nicer airline as well, but the main justification was the airport. About £20 of the cost was mitigated by not having to travel to another airport on the outskirts of London (with the exception of the ~£8 journey to and from Heathrow)
Spent £50 more (a 10% fare increase) to fly to and from London Heathrow Terminal 5. The terminal opened in 2008 and is very modern. Baggage reclaim seems faster than other airports I've visited, the overall layout is more sane and security tends to move quite fast for an international airport. It's certainly worth a little extra in my opinion.
There's room for improvement. I still prefer the 4 hr 30 train journey from London to Edinburgh v. the similar priced 1 hr plane journeys. Air travel might win if it can beat the convenience of just turning up at the train station 20 minutes before the train leaves, only paying a small extra fee if I want the freedom of using any train that day instead of a specific train and compete with the fact that the train stations are in city centres, whereas the airports are on city outskirts. These problems are quite hard or impossible to solve, so it's going to have to try harder in other ways. Oh, and the trains have (somewhat spotty in parts) wifi as well.