The reg checker is live: you can already look up any car's MOT history and verified mileage free. Zone-by-zone ULEZ answers are being added to it; until then, the rules below cover most cars.
The quick rules
PetrolEuro 4 · registered from roughly Jan 2006 → usually free
DieselEuro 6 · registered from roughly Sep 2015 → usually free
Electric / hydrogenalways free, every zone
Non-compliant£12.50/day in London · varies by city
"Usually" because the standard is set by what the manufacturer certified, not the date alone. A handful of models met it early or late. The per-reg check will settle it exactly.
Where the zones are
London ULEZall London boroughs · 24/7
Birmingham CAZcity centre · charges cars
Bristol CAZcity centre · charges cars
Bath · Sheffield · Bradford…charge vans/taxis, not private cars
Zone rules change. This table is reviewed with each data release. Source: TfL and local authority schemes.