Your reply is more akin to that of a Political Party Broadcast and sound bite for one of the various political parties voicing their woes against the EU and Europe in general. There is no "super-state" that you refer too, if that were so, then the fall of the Euro, the mass exodus of transients passing through various boarders etc. would not be so. So, in truth you are in reality an anti-European and anti-EU rules person which really as noting what soever to do with your argument as any invasive species requires control, be it human, plant, animal, insect etc. and this has been going on since time and planet were a mass of chemicals and so on. It is not a new thing.
In answer to your question Common Law - the law common to all men
In the UK it is assumed that all actions are deemed to be legal unless the law prescribes otherwise
You have not answered the question, just given a layman's term of what your interpretation of "common law" is. You refer to the UK but that in itself is factually incorrect, as English and Scots laws differ to each other with Scots law being older and covering various groups of law to make into one (such as Roman, Anglo).
So which part of law and can you name the parts you refer to please.
Given that you have Civil; Criminal; Statute; Case. with all its sub divisions such as Tort. "Common" law is that law made through principles established in cases over the centuries during the standardization of laws throughout England and Wales from the eleventh century onwards and upto the modern era.
Scots law which differs to English law (not UK) is laid out as such: Feudal Period; Dark Age Period; Roman Period and Modern Period. [General Principles of Scots Law. Enid A. Marshall 1 -7 editions] Under the Modern Period, this is seen as when both nations moved to use each others laws, especially under the Act of the Union. English law starts from when the Anglo-Saxons started to be part of the English shires. After the Norman Conquest, you had the various levels of courts; with the Saxon shire courts, the feudal courts of the barons and the ecclesiastical (church) courts. From the 17th and 18th centuries, common law absorbed the Law Merchant, the international code of mercantile customs, which included ships and all their goods, alcohol and all things worn and used. During the 19th century virtually the whole of English law was reformed by legislation.
Under various "Common Laws" such as the laws regarding "Commoners" which my late grandparents passed that to the family still use within the New Forest is a very unique set of rules, and only a few forests apply. So I ask, can you please be more specific as to what part of "common" law is it you refer to, please name that part of law.