Parliamentary supremacy prevents judicial review of local domestic law. However in the late 20th and early 21st century, the theory of parliamentary supremacy underwent erosion from four directions. The first is the devolution of power to local assemblies in Scotland and Wales.
The second erosion has been in connection with institutions of the European Union, in particular the European Court of Justice which asserts the power to exercise judicial review over UK law. In this situation, an adverse finding by the Court that a UK law is inconsistent with the Treaties automatically annuls the law, since the European Communities Act provides that European Community law is supreme in the United Kingdom.
The third erosion has been in connection with the European Convention on Human Rights. The European Court of Human Rights can find acts of the UK government (including those done pursuant to an Act of the British Parliament) to be in violation of the Convention. However, decisions by the ECHR (unlike decisions by the ECJ) does not automatically annul the law; the Government must introduce a bill into Parliament to implement the ECHR's decisions.
The fourth erosion has been due to the incorporation by the Human Rights Act 1998 of the European Convention on Human Rights into UK law. Acting under the Human Rights Act, British courts can declare Acts of Parliament to be in violation of the Convention. This power, like that of the European Court of Human Rights, does not automatically annul the law. However, unlike the ECHR, the British Courts have a formal procedure for the review of Acts (technically the ECHR reviews acts done by the member state, which can include both legislation but also other government actions, but the two are not distinguished), resulting in a Declaration of Incompatibility. The Declaration of Incompatibility does not annul the law, but enables the Government to use an accelerated procedure to enact a bill to repeal it.
However, in each case, there is no theroetical erosion of Parliamentary supremacy. Firstly, the Parliament may abolish any of the devolved legislatures at its pleasure. Secondly, the European and British Courts have the authority to declare incompatibility or to annul a law only because of an Act of Parliament, which can be repealed by the Parliament. Thus, theoretically, Parliament remains almost entirely sovereign. (The qualifier "almost" is provided because in the 1920's, after years of dispute, Parliament finally agreed that it does not have sovereignty over the Church of Scotland, the established church in Scotland.)