The concept of Parliamentary sovereignty has been a subject of much public discussion in recent years, in particular in light of the 2016 referendum on exiting the EU and the subsequent events.
There has always been some tension reconciling Parliamentary sovereignty with the supremacy of EU law.
Currently section 2(1) of the European Communities Act 1972 provides that the laws of the EU are to be given legal effect in the UK. Read along with section 2(4), this means that the UK Parliament is obliged not to legislate in a way which is contrary to EU law.
The doctrine of supremacy of EU law has the effect that EU law takes precedence over a conflicting provision of national law (irrespective of which law was made first in time). So, in the important Simmenthal case, the Court said:
“…every national court must, in a case within its jurisdiction, apply [Union] law in its entirety and protect rights which the latter confers on individuals and must accordingly set aside any provision of national law which may conflict with it, whether prior or subsequent to the [Union] rule.” (Case 106/77 Simmenthal II  ECR 629, paragraph 21)
This principle was confirmed by the UK courts in the case of R v Secretary of State for Transport, ex parte Factortame (No. 2)  3 WLR 818 in which it was held that:
“If the supremacy within the European Community of Community Law over the national law of member states was not always inherent in the EEC Treaty it was certainly well established in the jurisprudence of the Court of Justice long before the United Kingdom joined the Community. Thus, whatever limitation of its sovereignty Parliament accepted when it enacted the European Communities Act 1972 was entirely voluntary. Under the terms of the 1972 Act it has always been clear that it was the duty of a United Kingdom court, when delivering final judgment, to override any rule of national law found to be in conflict with any directly enforceable rule of Community law.”
The UK courts therefore have to disapply UK law if it is found to be inconsistent with EU law.
In its case law on this issue, one line of reasoning adopted by the European Court of Justice is that, when entering into the European Union, Member States transferred some of their sovereign powers and rights to the EU institutions, thus giving those EU institutions the ability to create law which binds both individuals and Member States.
There is clearly a tension between the doctrine of supremacy of EU law on the one hand and the doctrine of Parliamentary sovereignty on the other. Some commentators consider that the UK’s joining the EU had the effect that Parliament permanently gave up some of its sovereign powers to the EU. However, in constitutional theory terms, Parliament remains sovereign since it can repeal section 2 of the European Communities Act 1972, as it has done so in section 1 of the European Union (Withdrawal) Act, the effect of which will come into force on “exit day”. “Exit day” is defined in that Act and is the day the EU treaties will no longer apply to the UK (see here for more information). Until that repeal takes effect, EU law will continue to have effect in the UK as described by this page.