The current level of car use isn't able to be maintained at the current level long term due to the use of limited resources and also climate change concern so it is not sustainable. Hydrogen is all very well but extracting it uses a lot of energy. It may be that the days of the private car are numbered as it will never be as effecient as public transport so we should start planning for a possible future without the car.
The M11 can easily be accessed from East London. If you improve the A1(T) then you will only end up with encouraging a lot more traffic to use the route and you may find that it soon is at capacity. Baldock to Alconbury would as I say be quite expensive to do and if all it does is increase traffic on the rest of the road so that it can't cope then it's pointless. You could get some extra capacity on the M1 through Active Traffic Management without having to do any actual widening. A high speed line to the North will also likely result in modal shift to rail away from the M1.
Public transport is actually highly inefficient from a number of perspectives.
It works in certain circumstances (probably <20% of passenger journeys).
It does work for getting people into and around large conurbations - of which I'd say the UK has about 5 - Greater London, West Mids, Greater Manchester, Tyne & Wear (at a push) and Greater Glasgow.
It doesn't work particularly well outside those areas. My commute from Northampton - MK is totally impractical by public transport - let me explain:
I live at the east end of Northampton - the bus into Northampton town centre takes about 35 minutes and deposits me at the bus station, 15 minute walk to the railway station before a 15 minute train ride to MK and 10 minute walk to the office - grand total 1h 15 mins assuming perfect connections to cover a 26 mile journey which I can drive directly in 35 minutes.
The days of the private car aren't numbered - far from it. You cannot force people away from it and public transport simply can't work for the vast majority. What you can do is offer public transport as an alternative for those who want to use it.
Extracting hydrogen isn't straightforward - at the moment, but as ever the more we do it the more efficient we become at it. Your argument seems to be as it's difficult we shouldn't do it - follow that logic to it's logical conclusion and we'd never have developed nuclear power and never moved beyond the horse & cart.
As for your A1 / M11 comments, all I can say is your taking a knee-jerk anti roads line. You clearly don't live in the area or use any of the roads in question. I used to and there would be widespread support in many places along the A1 to it being upgraded, not least because it would save people travelling 10-15 miles out of their way to pick up the M1 on the belief it is a better road to take you North.