Old/new it does not matter.

> I picked towns that are almost exact equivalents for Henley, except that Henley has not bothered.

Well, that's my point, isn't it? Glad we agree... The thing is that it is difficult to resolve when that has been the case for decades, if not centuries because it's like that everywhere and you cannot decide to re-do half the country's road network and to raze everything that's in the way, especially in the UK.

19th century Paris: They did raze a large part of the city to make way for new avenues. 17th century London: After the Great Fire they rebuilt following exactly the previous narrow roads because no-one wanted to lose an inch or pay for an inch, and it's still the way any new projects are welcomed...

>The thing is that it is difficult to resolve when that has been the case for decades, if not centuries because it's like that everywhere and you cannot decide to re-do half the country's road network and to raze everything that's in the way, especially in the UK.

My point is only that this is exactly what the Netherlands has already done, which shows that it is perfectly possible to resolve (and, in general, without any razing - the Dutch are at least as proud of their history as the British)

The fact that the Netherlands looks good now is because these exact same problems have been solved over time. The UK could even benefit from an easier time, since it gets to just copy the best-working solutions.

To respond to your edit.

19th century London: they razed whole neighbourhoods to construct the Underground.

21st century London: they propose to raze the St Pancras estate (with compulsory purchase orders) to build the HS2 railway.

But cycling doesn't require razing: the solutions I have given to your suggested problems don't raze a single thing.