If your vehicle is 40 years old (or greater) and classed as 'Historic' or more it is exempt from paying for RFL. You still need to apply for it from DVLA (but it is 'free').
Best read this and act on it if you need to.
Historic (classic) vehicles: MOT and vehicle tax
Congestion Charge. This still applies to 'Historic' vehicles - you'll need to register it with TFL if you want to pay on line.
If the car is registered as 'Historic' and recorded as MOT exempt then you
will not currently pay ULEZ (which operates within the North and South Circular A206 roads). This does not replace the Congestion Charge - ULEZ (if applicable) is paid 24/7
in addition to any applicable Congestion Charge.
Khan wants to extend ULEZ to all London Boroughs at some point in the future - the London Assembly has voted to agree to this, however there are a number of individual London Boroughs who are opposed to this £12.50 daily levy on non compliant vehicles.