You’re right on the polarised debate. Those who want safer cycling deal with people on the one hand saying nothing needs to change and on the other people saying it’s so dangerous they’d never cycle.
Better public transport isn’t something I’m going to argue is a bad idea but how to do that is a whole different question - other than (hugely expensive) tube lines, anything you do is going to take space that's currently used by private cars. Doing that is going to, using the language used to criticise LTNs, cause huge traffic jams, displaced traffic, 'make lives impossible', be a 'war on the motorist',
The anti-LTN crew in Lewisham thinks a tram on the south circular is the alternative answer. That's would cause massive displacement of traffic - how would a tram not get delayed on all the single lane sections of the A205 unless the other traffic was directed through other (smaller) local streets? And it wouldn't make my trip to Dawsons Hill any quicker because it still wouldn't be door to door - 20 minute walk to a stop on the A205 (walking to Brixton Hill and getting a bus doesn't save any time). 5 minute wait for a tram? 10 minute walk at the other end. The tram would still be slower than driving off peak on the same road as it's got to stop for passengers. Suddenly it's not going to actually be any quicker than taking the bus is now.
In outer London the Superloop express buses might help. But it's probably still going to take you 30 minutes to get the train to Croydon and then an express bus from there to Bromley and likely a local bus to your final destination. Again, probably not that different to your current public transport trip - it might shave off 10 minutes or so but unlikely more.
The Superloop is part of the Mayor's plan to improve outer London's bus network, connecting outer London boroughs, faster.
www.london.gov.uk
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You've mentioned surge pricing above - now some form of variable charging for road use would absolutely reduce private traffic. But the response to ULEZ would be nothing compared to that for road pricing set high enough to actually discourage car trips. It's simply not possible to completely overhaul public transport BEFORE reducing car traffic - as you need to get rid of a load of the cars to speed up the buses.
A question for you - how much would the cost of your driven trip to Bromley have to be before you would use public transport instead?