All cars over 40yrs old require an MOT, most pre 79 diesel cars would have been minicabs and will be long gone. There won't be many 40yr old plus diesels left on the road. Diesel cars still have to pass a smoke test and not just at idle, they are also revved up, they just aren't revved as high as petrol engines as diesel engines have a lower rev limit.
Most cars emitting a cloud of black smoke only do so because the car has been driven around town slowly and the soot has built up in the exhaust, the next time the driver puts their foot down and all the soot comes out in one go. From then on the exhaust should be clear until the next time soot builds up in the exhaust. If the engine continues to smoke, it is a good chance that the injectors are worn, this can lead to over fuelling and the engine is unable to burn it properly.
Why do injectors wear? That is partly down to cheap supermarket biodiesel which doesn't keep the fuel system as clean as the more expensive fuels.
