I lived in London for a year. It was the most lonely isolated place I've lived. Also it's not really part of the UK anymore. It's a "world" city - which makes the feeling of loneliness even worse.
Yeah well, that's pretty much all big cities when you arrive on your own, especially after student age. It's also very expensive to move around, and at this it's one of the worst places.
London is cheaper to move around by public transport than many other British cities.
A bus or tram journey is £1.45 regardless of distance, but in Manchester a tram journey is over £3, in Birmingham over £2, in Edinburgh £1.50.
London's tickets are also much better integrated -- only a couple of express train services to airports have special fares, and they all have non-express, cheaper alternatives.
There may be worse places in the UK, I honestly haven't compared that much with medium-sized cities like Manchester or Birmingham.
Among international big capitals (which is what you can really compare London to) it has to be the worst. The fact that going to other cities in the UK is prohibitive makes it even worse (it's cheaper to fly to many places in Europe than going to most other UK cities by any means of transportation). If you want to move medium distances within London in reasonable time, it's tube/Overground/DLR and it's prohibitive. Using the Oyster card it's better but still rubbish really.
The example is stupid and sensationalist, those stations are the two closest at 260 metres apart, or about two train lengths.
Like many European cities, paying by cash is being phased out. It's annoying for visitors, but London is ahead here: Oyster cards are refundable, let the user go overdrawn (into the deposit), and contactless credit/debit cards are accepted.
The actual Zone 1 fare is £2.20. A central zone Berlin ticket is €2.60. Copenhagen ~£2.60. Munich €2.60.