Some scaremongering going on there.
The lack of equivalent petrol cars would push up the prices of those but there's too many diesels around and too few petrol.
It doesn't address the use of the very same engines in many commercial vehicles. Pushing up costs to business would drive them out of those cities.
I can't see those cities that depend are car manufacturing cutting off their noses and all that.
The oil industry will have to rebalance it's supply chain, which I suspect can only be done to a point. There would come a point where diesel which to a large degree is produced as a by-product would become oversupplied and hence reduced in price.
Authorities can't make point based and simple decisions in isolation. You end up with unintended and frequently negative consequences.
Top end cars will continue to use diesels (the same ones as commercial vehicles) because the manufacturers need to keep the volumes up. Owners of those top end cars will simply buy a city car too to go to work thus reducing the pool of petrol cars and remove them from those who need them. Market forces will create a situation where a simple decision (quite well founded on an environmental perspective) will make those cities inaccessible by car to many.
It will take a great many years to change things. Do it quickly by a single policy and some cities will become ghost towns or accessible only by the very rich because individuals and businesses can't afford to go or work there due to a policy wonk.
It all needs carefully crafted and joined up thinking. Something no-one in this country seems able to do because it costs.