Change will be slow, but it will happen. Following 2030 car numbers will start to dwindle - not only are there insufficient materials to replace every ICE car one for one with a battery car, that relative rarity will elevate prices beyond the reach of many. In addition, most other western markets will be scrabbling for those same resources, further elevating prices.
Whether or not national or local government does anything to make cycling more appealing and more mainstream is uncertain. However, the end of the age of the motor car as king is now within view, as is the end of unfettered, unrestricted personal car use. With seriously reduced car numbers and a proportionately higher number of cyclists the government will be forced to start giving us some consideration as a user group. Hell, I may even live to see it.
As for London, there is a significant proportion of londoners that would sooner sit in a car for 40 minutes than walk for 10. Hell, in greater Manchester the average car journey is now less than 1 kilometer (yes, 1000 metres, 1200 odd lazy, casual paces) distance and I don't suppose Larndon is far behind. The future of London is in the hands of its own people and their own outlook and motivation - what happens there will be down to them and no one else.
The whole LTN thing is a joke. Not the concept itself, but the manner in which it is being considered. When trying to reduce crime the police aren't forced to take into account the views of bank robbers. When fighting cancer the scientists aren't forced to take into account the views of the Marlboro Man. Yet one of the factors determining the success, and the ongoing existence or otherwise, of LTN's is a public consultation involving the views of motorists, the very people causing the congestion, the pollution and the danger. It's madness - they are the disease, yet they are being allowed so much influence over the cure.
Don't vote in twits for mayors, eschew the car, start riding bicycles. Simple really, and it always has been. This idea that the future relies on government schemes of various sorts is rubbish - it'll change when Londoners really want it to, and not a moment sooner.