Kindly see the boldening below. It baffles me because
the UK doesn't have a SEPARATE Constitutional Court, unlike France or Germany.
Isn't the Administrative Court a Constitutional Court?
The work of the Administrative Court comprises the administrative law jurisdiction of England and Wales. Its varied work is directed at the lawfulness of the acts and omissions of central and local Government, regulatory and disciplinary bodies, inferior courts and tribunals, and other public bodies and officials exercising public functions. The Administrative Court has both a civil and criminal jurisdiction.
This supervisory jurisdiction is exercised in the main through the procedure of Judicial Review (JR) – a wide and still growing field.
Note that I'm quoting from the EWCA judgment, not the UKHL one. Jackson & Ors, R (on the application of) v HM Attorney General  EWCA Civ 126 (16 February 2005).
The reality is that the 1911 Act was a most unusual statute. By that statute the House of Lords, the House of Commons and the King used the machinery of legislation to make a fundamental constitutional change. Nearly 100 years after the event, the court has been invited to rule on the precise nature and extent of that change. We have decided that it was right for the Administrative Court to accept that invitation. The authority of the 1949 Act purported to be derived from the 1911 Act. The latter Act, by s.3, expressly envisaged the possibility that the validity of subsequent Acts enacted pursuant to its provisions might be subjected to judicial scrutiny. The effect of the 1911 Act was undoubtedly susceptible to judicial analysis. However, in considering that effect, the Administrative Court was acting as a constitutional court. There was no precise precedent for the jurisdiction that it was exercising.