The rules are very clear, exempt or not, if your car fails an MOT it is deemed unroadworthy.
Your car could have failed the MOT on emissions which 40 yr old + cars are not going to be subjected too - so not technically unroadworthy from next year.
There are a lot of points that can fail an MOT that most sensible folk would not consider make the car unroadworthy, for example a 1" diameter rusthole in the boot floor or a big chip in the screen, or a front passenger door that can't be opened from inside, or a blocked washer jet. On emissions, the car will be tested (if presented) according to existing rules governed by year of manufacture (not whether it's over 40 years old). A 76 car would still be tested to 4.5%CO and 1200PPM Hydrocarbons same as it always has been, whereas a 75 will only need a visual smoke check, so the old iniquities remain! Honestly, if you can't get your Dolomite below those figures, there is something seriously wrong! In theory, a roadside emission test that gave a result over the MOT test limit pertinent to the YoM of your car could still render you liable to prosecution even if the car is MOT exempt! This is an admittedly unlikely scenario, but it IS possible and with the powers that be focusing increasingly on so called "dirty" vehicles, it is only going to get worse!