As we write this on 27/04/18, were cars to be included in the CAZ scheme, the only non-chargeable diesel cars will be Euro 6, although there maybe a temporary exemption for Euro 5. Petrol vehicles will be exempt from Euro 4 onwards.
You can check the class of your car at the RAC website. You have to agree to a valuation and the class appears in the title of the valuation sent to you by email.
Buses on routes 6, 6A and 7 are due to be made Euro 6 compliant this summer.