90% of UK journeys are less than 5 miles, so well within cycling distance.  In London cycling would actually be faster than most other means of transportation.

On bicycling and climate, it doesn't seem to bother the Danes or the Dutch!  I grew up in Toronto, which is a genuinely inhospitable climate to cycling (too hot and humid or too cold): there aren't 10 days in London which are as bad, in an entire year.  It's all a matter of your reference point.  Given congestion, there really aren't ways of getting another million of us (projected population rise to 2030 I believe) around London.

(I should add, for safety concerns, that I never cycle in London)

Buses.  You have captured the 'middle class British' view perfectly.  Whether Maggie T really said 'anyone over 24 who takes a bus is a loser' or not, I don't know, but the sentiment caught the zeitgeist.

but our dear Mayor has engineered a '4% modal shift' from cars to buses, via the congestion charge.  I don't know if you live in Central London, but I do.  Buses have become a preferred method of transportation (pace the bendy bus, which drives me nuts), even for middle class professionals.  Particularly given what has happened to the Tube (tube journeys have doubled since the late 80s-- arguably a victim of its own success).

There has never been a 'to bus' modal shift recorded in history.  Yet London has managed it.

I expect, in time, that will percolate around the country.  But congestion will have to get much worse, and local councils much tougher.  Not everyone has its own home-grown anarchist-trotskyist demagogue.

Light Rail the Treasury has put the brakes on, because they don't see the cost-benefit working out.  Manchester nearly lost its extension (I think they clawed it back politically).

For sure we should rebuild the Camden Town to Elephant and castle tram line (the one that ran down where the tunnel is at Holborn-Kingsway).  But it's not even on the strategic plan, AFAIK.  Uxbridge Road is the next one.

Water level: before the current drought, the concern in London was that the water level was rising due to less industrial offtake (industry in London almost gone).  The Tube has had recurrent flooding problems.  (my father built some of the original flood doors on the Northern Line-- the plan was to shut them in case of a nuclear war, you can see the grooves in the floor where they would swing.  I think of them fondly every time I walk by them-- son and father connected by 55 years).

If sea levels rise, and we get more flash flooding, then London's underground system is quite vulnerable.

My understanding is New York could use 'cut and cover' subway construction because the roads were wider, and the ground better.  Most North American subways were built with 'cut and cover' it costs something like a 10th of tunneling.

One of the reasons the Picaddilly Line wobbles the way it does is that apparently they couldn't buy the foundation rights from the freeholders, they had to literally dodge some buildings in South Ken and Knightsbridge.

On Sprawl, the Deputy Prime Minister is laying plans for 250,000 new homes in the South East-- Thames Gateway, also Milton Keynes, Northampton and a few other places.  sprawl is very real, and very British.  Agree its less than an American city.