Why else would a 1967 or 1971 MGB (GT) be listed as tax exempt?

Certain vehicles constructed before 1st January 1973 are exempt. They will be in the 'Historic Vehicles' class.

Vehicles built before January 1st 1973 are exempt from road tax payments, but you still need the disc in the windscreen. Also note that it's cars BUILT before that date, not registered, so quite a few cars registered in the first couple of months of 1973 can still get free tax if you can prove the build date.

The website doesn't list tax exempt as old vehicles are not technically tax exempt, you still need to get a tax disc but your road tax costs £0.00. I believe this is done so that you still have to provide proof of MOT and insurance.

Crazy dog is right - there is a fixed date, before which vehicles have their road tax for free - there isn't a 'sliding scale' of age for vehicles, it's a firm cutoff.

Any vehicle that qualifies still needs to display a tax disc or be declared SORN, the same as any vehicle does now, it's just that if you have a current MOT & insurance, you may tax the vehicle for free.

Vehicles built before 1973 are Tax Exempt, as are fire engines, possibly Emergency Ambulances, but not sure.

Tax exempt means that the car was first registered before road tax was around. Road tax came around at the end of 1971 so all cars that were registered before that time are tax exempt. (you still require a tax disc but the price is £0.00)

The car is over 25 years old and therefore is Tax exempt, a tax disc is still required.

I believe once a car reaches 20 years old it becomes tax exempt.

Pete is right and you should be able to get classic car insurance for something that age, which is a lot cheaper than standard insurance