Definitely better than it was 10 years ago. I've visited London once every 1-6 months for the past 10-15 years, and have noted a change. It's still not amazing, though - honestly, if they were to aggressively disincentivize diesel in small cars, I feel like everything would be fine. Subjectively, a day in London seems akin to spending a few hours with a 50cm3 2-stroke chainsaw, or an hour on an old diesel excavator. I do not feel the same way about most US cities, nor even most cities in mainland Europe.

That would be the tube. I cycle everywhere in London and only get black bogeys on the tube. It's brake dust, mostly.

That was more of a trip on the underground thing

You know, I think that has. I remember this happening, but the recent years I’ve been into London on occasion, this doesn’t seem to be a problem anymore.

Some argue that these coarse particles are less damaging for your health than the finer particles we are exposed to today, even if you cannot see them settling as dirt.

Although on that part tire abrasion is probably even a larger factor than exhaust particles, even if it doesn't smell as badly. Some say the factor is beyond 1000x for tire abrasions. Info is hard here, because many sources have their own ball in the game.

But cars today are significantly more heavy, which increases these abrasions nonlinearly.

That’s usually associated with brake dust inhaled while on the Tube

Still snot, but not as black

(I live in the countryside so I notice air quality quite a bit when visiting. I rarely have to blow my nose at home)

Yes as long as you stay off the deeper parts of tube, e.g the Northern Line. One of London’s biggest sources of particulate pollution is now tube train brake pads

I'd say so for sure. I've lived in London most of my adult life, and in my experience the air is a lot better than it used to be.