Exactly, but the UK laws that adopted EU law became the law by Act of Parliament. One of the most controversial examples is the Human Rights Act 1998, which is a UK law that pretty much adopts EU law pretty much word for word. Even before Brexit, Cameron had pledged to repeal the HRA and replace it with a British Bill of Rights so it's pretty clear that British law doesn't have to adopt EU law word for word. Every EC or EU treaty was ratified by Parliament too. The relationship, between the UK and the EU, firstly, is consensual, and secondly, that Parliament subcontracts its sovereignty and therefore, has the power to take that back. Astute thought his link stating the 'influence' of EU laws and regulations on the UK was a trump card. It wasn't, because even post-Brexit, our laws will be influenced by the EU -- civil servants are more or less rewriting them word for word before we leave, making adaptations where necessary. The sovereignty of nation-states is eroding because of the impact of globalisation, and the 40-odd free trade deals Liam Fox will reduce sovereignty in a similar way to how the EU does, the extent may vary, but ultimately free trade prevents a Government from introducing tariffs, for example. To demonstrate this example, the Canadian Government has had legal action taken against it by (mainly) US corporations because of Canada's environmental regulations and public healthcare system -- 70% of legal action taken through NAFTA has been against the Canadian Government.
Parliamentary sovereignty as a doctrine means there are no limits to the powers of the UK Parliament and in practice, it can pass whatever law it likes. The first misconception is that the EU needs to approve UK law, this is not the case, because the EU plays no physical part in the passage in our lawmaking process (from First Reading to Royal Assent). Secondly, because Parliament has unlimited power and the EU has no means of physically blocking any legislation that passes through Parliament, some have erroneously taken this to mean that the UK can do whatever it wants within the EU. Evidently, this is not the case because of numerous breaches to EU law and regulations would open up a process in which the EU can sanction a member state, or expulsion if sanctions do not have the desired effect. But, the ultimate question is this: does the UK Parliament have the power to pass legislation that contradicts EU law and regulation? The UK may get sanctioned, or expelled from the EU depending on the severity of breaches, but the answer to that is yes. The example of Hungary proves that the supreme sovereignty still rests with the nation-state because the Hungarian passed its Soros Laws, despite condemnation from the EU. I disagree with the Soros laws (and numerous Hungarian laws, frankly), but this example is important in highlighting my argument.
