Breakdown of public finances shows how taxes and public spending are used to narrow north-south divide
www.theguardian.com
London(ers) paid in £26.5bn more in taxes than got spent in London (in 2016/7, ONS figures). There's plenty of other sources you can check this from if you want to.
On public transport specifically you are right- London gets far more money than any other region does but in general they pay more in taxes than they receive in government spending - and you drew the comparison having been fined which is why I said that.
In terms of the LTN - there have been LTNs built all over the country so it's not just a London thing, and all modern housing estates are built to the kind of design that LTNs seek to replicate - a series of cul-de-sacs with feeder and boundary roads. You can still travel on railton road, you just have to enter/exit at specific points that means you can't use it as a through road anymore. You still have the right to travel on that road, just not enter from specific places/directions in your kind of vehicle. LTNs aren't the only example of this, there are bus gates in plenty of places.
As an aside, the main benefit of HS2 is not the time saving - which does get significant if it gets to Manchester and beyond - but in extra capacity, this has been really badly missold. For instance, in Birmingham itself, once HS2 is running, we'll get 8 more slots per hour at Birmingham New Street for local trains, as the existing fast services stop. We'll also be able to put in more slots per hour on some lines because you can time trains more closely if they are all moving at the same speed. This kind of effect will be replicated in other places that HS2 serves. That will make a huge difference to local journeys in the region and is far more valuable than the time saved on journeys to London.