In the UK cars over 40 years old do not have to follow exhaust regulations as long as they have registered as a Vehicle of Historic Interest.
Any vehicle in the UK that is over 40 years old can register as a Vehicle of Historic Interest. You can find the process to do so on the UK government website here. but the short version is you fill in form V112 at the post office. You can apply for this as long as your vehicle has not had significant changes made to it in the last 30 years.
Once you have done so your vehicle is no longer required to pass an MOT inspection and as the exhaust emissions test is part of the MOT you will no longer be measured against it. You will also no longer be required to pay Vehicle Excise Duty, more commonly known as Road Tax, although you will still be required to be registered for tax. When you register you will be sent a refund for any unused road tax that you have already paid for.
You should remember however that just because you no longer have to have an MOT, this is no excuse for having an unsafe vehicle. You are still legally required to keep your entire vehicle in a roadworthy condition, driving with broken lights, bald tires are anything else mechanical which would cause an MOT fail would usually still be illegal and if your exhaust is particularly noisy or smoky the police will still deal with you for causing a public nuisance.
You can of coarse still have an MOT, whilst not a requirement it does provide independent proof that your vehicle is safe, and if your vehicle is suddenly producing noticeably more exhaust then normal, you should definitely have the vehicle looked at to ensure there is no risk to you, the vehicle or anyone else.