Jeremy, there is no need to have air quality monitors covering the entire area; this can be modelled using traffic data. See map based upon 2016 measurements.
If you are of the opinion that concentrating pollution along certain roads is unfair, then that would imply that the 75k-100k vehicles per day using the A4 should be more evenly distributed.
So what about doubling traffic along Chiswick High Rd to 25k and other roads need to share the load as well, so there should be 5-10 times more traffic than there is at the moment along routes like Wellesley Rd.
Clearly that is a nonsense, which illustrates the flaw in your thinking.
You can either believe that all roads are the same and it should be a complete free-for-all for drivers, or, there is a difference between different types of road and it is a responsibility of Highway Authorities to manage traffic based upon a hierarchy.
The A4, A316, S Circular are part of a defined network called the Transport for London Road Network (TLRN) and I believe each borough will have a defined principal road network within the borough as well. This will be approximately aligned to the 'A' road network but not exactly. For example, Wellesley Rd is probably still listed as the A3000 in some maps and that won't be part of the Hounslow principal road network.
The basic principle adopted by the Highway Authority is that traffic should stay on the principal road network as far as is practical. So there is no way traffic should be cutting between two TLRN roads (A316, A4) along roads that aren't even part of the Hounslow principal road network although how this is done isn't a simple question.
If you are concerned about public health, then the focus should be on reducing the number of polluting vehicles in the first place, not juggling with the road network.
And even if every single vehicle on the road was zero emission at the tailpipe, you are still left with the challenge of managing the road network and large volumes of traffic are simply not appropriate for roads not designed for it.