Just being a tax exempt heritage registered vehicle doesn’t mean it is automatically Ulez exempt.
You can check your vehicle by registration here; Check your vehicle (tfl.gov.uk)
The official line; To help clear London's air, the Ultra Low Emission Zone (ULEZ) expanded on 29 August 2023 and to cover all London boroughs. This will bring the health benefits of cleaner air to all Londoners.
The ULEZ operates 24 hours a day, seven days a week, every day of the year, except Christmas Day (25 December). Drivers of vehicles that don’t meet certain emission standards need to pay a daily charge to drive in the zone.
Before the London Ulez expanded to the Greater London area it generated over 53 million ponuds of revenue for cash strapped TFL.
ULEZ Ultra Low Emission Zone is Greater London’s Clean air Zone. Birmingham, Bristol also have car affecting clean air zones.
Vans, Minibuses, taxis and cars need to have at least Euro 6 emissions for Diesel and Euro 4 for Petrol. Generally, 2016 for diesel and 2003 for petrol, with some Japanese cars as old as 1999 meeting the emissions levels.
Classic and vintage vehicles over 40 years old qualify for exempt if they are registered historic and not used for business. This however does not automatically mean your vehicle is exempt.
If your vehicle flags as not being ULEZ compliant you can register with TFL get your historic vehicle exempted. Register a vehicle for ULEZ and LEZ - Transport for London (tfl.gov.uk)