ULEZ isn't about climate change or the environment, it's nominally about air pollution. But scratch beneath the surface, even a little bit, and you'll realise it's not remotely about that either.
Diesel vehicles have lower CO2, HC, and CO emissions than petrol vehicles while petrol vehicles are have lower noxious gas and particle matter emissions. So diesels are "better" for the environement and petrols "better" for health. Of course this only considers tail pipe emissions and ignores other sources of air pollution from vehicles such as particle matter from break, tyre, and road wear. All of which are impacted by weight, driving style, road conditions, and the quality of the parts in question.
It gets even more absurd when your realise how vehicles manage tailpipe emissions. Since about 2009 for diesels and 2016 for petrols, vehicles been fitted with diesel / petrol particulate filters (DPFs / PPFs) which trap some exhaust gases in the filter, resulting in lower tailpipe emissions.
Sounds good, except PFs are designed to "regenerate" periodically. This is essentially a process where the vehicle raises the exhaust gas temperature to burn off all the trapped particles in the PF and expel them out the tailpipes.
Usually the conditions required for this to happen are only met during a motorway driving so the emissions aren't actually reduced, they're just stored and dumped all at once at a later date.
And this is before you even start to consider the wider issues of building new v extending the life cycle of vehicles and how that impacts on the environment and resources.
As I said ULEZ has sweet FA to do with the environment, climate change, or health.