Having abolished the Law Lords in the service of the peculiarly American theory of the separation of powers, They presumably also wish to abolish all quasi-judicial functions of Ministers or of local council chairmen, as well as the role of the judges in making the whole of the Common Law, and much else besides. All because of something that They once heard on The Wire, or The Simpsons, or whatever.
And then what? As will eventually be found to be the case, both trial by jury and trial by magistrates are contrary to Their other pet cause, the jurisprudence of a foreign court interpreting a foreign document. They, who object to the quasi-judicial powers of Ministers accountable to Parliament, also loathe both juries and magistrates, and for the same reason, namely hatred of the people at large.
Without a resolution of the House of Commons (itself elected more proportionally and from candidates selected by means of something like an open primary system), no ruling of the European Court of Justice, nor or of the European Court of Human Rights, nor of the Supreme Court, nor pursuant to the Human Rights Act, should have any effect in the United Kingdom. The High Court of Parliament is precisely that: The High Court of Parliament.
And as such, it cannot co-exist with a Supreme Court detached from Parliament and, being Supreme, both enjoying and, soon enough, exercising the right to strike down the Statute Law with no one to in any position to do anything about this monstrous overthrow of democracy and liberty.
The present judiciary is riddled with old Communist Party activists and the like from back in the day. As in the form of New Labour, a project which now controls both parties, the student sectarian Left of the 1968 generation has now staged its coup.