Blue badge holders are treated differently from registered wheelchair vehicles.
In many case a blue badge holder can drive a standard vehicle – those vehicles will have to meet the emission restrictions.
In London, Blue Badge holders will have to pay the ULEZ charge from April 2019 unless the vehicle has a disabled or disabled passenger tax class untill 2027 as @Volkswin says. You can also apply for a grace period if you are claiming disabled benifits such as PIP/DLA or armed forces benifits, as long as the vehicle is registered to the benifit holder or nominated driver.
WAV owners also have a similar grace period.
Londons ULEZ will be by far the most strictest.
There are 4 class types of Clean Air Zones outside of London A,B,C.D as detailed below:
A. Buses, coaches, taxis, private hire vehicles
B. Buses, coaches, taxis, private hire vehicles
C. Buses, coaches, taxis, private hire vehicles, HGVs, vans, minibuses
D. Buses, coaches, taxis, private hire vehicles, HGVs, vans, minibuses, cars. Local authority has the option to include motorcycles.
For example, Birmingham is a Class D zone, while Portsmouth is a Class B.
There are some national and local exemptions from the Clean Air Zone charges in cities outside London, You can contact the relevant authorities to find out if there are any local exemptions. The following are automatically exempt from national charges:
Ultra low emission vehicles
Disabled passenger tax class vehicles
Military vehicles
Historic vehicles
Vehicle retrofitted with technology accredited by the Clean Vehicle Retrofit Accreditation Scheme (CVRAS)
Birmingham, Bath and Portsmouth. Clean Air Zones are coming to Bradford, Bristol and Newcastle later in 2022, while the Greater Manchester CAZ is currently under review.