Just found a useful site - Transport for London - where you can check if your classic can enter the London Ultra Low Emission Zone
https://tfl.gov.uk/modes/driving/ultra-low-emission-zone/vrm-checker-ulez
Just enter your registration and hopefully you will find that your classic is exempt. There is also a checker for the T-charge or emissions surcharge. Again hopefully you will find you are exempt.
https://tfl.gov.uk/modes/driving/emissions-surcharge/emissions-surcharge-checker
However if I understand the rules you do have to pay the congestion charge. Maybe Roger Hogarth w