Common Law is not the law and is not binding in any country or area. You are bound by the laws that govern the place that you live. So for example, persons in Canada are bound by the laws of the Canadian Criminal Code.
Further, Common Law will never be the law in any country or area, anytime soon. Even if a billion people took the oath tomorrow, it would do nothing.
It does not matter if you agree or disagree with this - the fact remains, this is reality. You cannot opt out of the laws that govern the place you are living. There are no secret tricks or tips to get around this.
The head people in this scene will advise you as such - if you don't pay insurance, you should expect to face trouble from authorities. They will then go on to add the fantasy that if you join them, someday you won't have to worry about laws. Someday! Once they get enough people, they will magically take over the world. But that is not correct, and will never happen. If we follow historic precedent, the leaders of these movements end up locked up in jail more often than not. And that is the best option for them, and for everyone else. Jacquie might find herself a new concrete bedroom if she doesn't back down on this shit like yesterday, but what do I know right? I'm a "troll" therefore I can't know anything.
Take care and best regards. If something sounds too good to be true.. you know the rest. I've got a dozen or more examples of this failing in courts around the world, if you're interested.
MOT and Tax are advisable for safety precautions, but you don't have to contract with DVLA, they are a corporation, it can't be law that you have to register bwuth a corporation.