It would seem that a lot of UK universities will only revoke a degree in the event of "allegations of academic malpractice concerning work submitted for an award of the university". Basically, most universities (I checked Manchester, Newcastle, Swansea, London) will only revoke a degree if you are found to have cheated (via fraud or deception) in earning that degree. However, some universities, such as Birmingham, can revoke degrees for this reason and also if someone "is convicted of a criminal offence triable on indictment" (so if you had a criminal charge brought against you and were convicted of it).
So to answer your question, a) it depends on the university and b) it depends if the university revokes degrees due to crimes and if so, how serious the crime is (I doubt they would revoke a degree over multiple cases of bad driving. They probably would if you committed mass murder).