Not a whole lot will change after Brexit.
Have look at Page 26 of the consultation document.
The UK (and the EU!) are still remaining part of the UN-ECE regularity framework.
So its the UN that sets the rules!
More info here:
https://www.unece.org/trans/main/welcwp29.html
I cant see them retrospectively banning previously previously legal vehicles, it gets very expensive (for Governments/tax payers ) if they do.
Here are a couple of examples:
£200M (in 1833 money) to compensate slave owners, after slavery was abolished.
https://www.bristolpost.co.uk/news/bristol-news/taxpayers-bristol-were-still-paying-1205049
And almost £100M to ban handguns
https://ukshootingnews.wordpress.com/2016/08/02/britains-pistol-ban-cost-taxpayers-almost-100m/
But of course they could just make cost of ownership more expensive, as some cities are now doing.
"Diesel Gate" is even mentioned by name in the document, with recent raids on BMW etc, this is not going away anytime soon!
Either way NOx and particulate emissions are not good, but it could be resolved by rules that limit the miles driven by more polluting vehicles and allow them to stay on the road, who knows, I certainly dont!