There are two good tire options for the MGB. It is worth mentioning that MG chose to fit their MGB and MGB GT model cars with a 165R14 tire. They could have fitted wider lower profile tires from 1968 onwards but they chose not to because the car handled at its best fitted with a 165 section tire.
We would suggest that the best tires would be the 165HR14 Pirelli Cinturato CA67, which was original equipment. However the Michelin 165HR14 XAS is also an excellent period tire that will work well at high cruising speeds on dual carriage ways.
Many people will want to fit a wider tire of which we would strongly recommend not going any wider than 185/70VR14. And the best tire would be 185/70VR14 Pirelli Cinturato CA67, because the tire carcass is designeed to work along side a chassis design like the MGB. If you go lower profile than 70 profile then you should not fit inner tubes. And anything wider the 185 will spoil the handling.
MGB V8 Tires
Tire recommendation for the V8 version of the MGB is simple. Michelins 175HR14 XAS is the perfect tyre for the MGB V8. A larger section tire will not handle as well.