No; the courts have no standing to declare an Act of Parliament unconstitutional. The conventional wisdom is that this is not possible, Hope's remarks notwithstanding. This was established in Pickin v British Railway Board. Further explanation in Erskine May's page on the case, which summarises the principle as:
all that a court of justice can look to is the parliamentary roll. They see that an Act has passed both Houses of Parliament and that it has received the Royal Assent, and no court of justice can inquire into the manner in which it was introduced into Parliament, what was done previously to its being introduced, or what passed in Parliament during the various stages of its progress.
I suppose Lord Hope's comments leave open the possibility of a court attempting to review that situation in the future, but under the current understanding I don't think such a thing can occur.
Edit on pjc50's suggestion:
Factortame and Thoburn are possibly relevant cases which hold that there are particular pieces of UK legislation that cannot be repealed by implication. This is primarily that legislation which is enacted to comply with EU law, but also extends to other constitutional legislation like Magna Carta, the Bill of Rights, Human Rights Act and so on. The principle means that such law cannot be repealed through the enactment of further legislation that contradicts them; such legislation would be subject to ordered to be disapplied by the courts. This principle does not prevent Parliament from passing an enactment that specifically alters or repeals a prior Act in order to achieve whatever it is that they're wanting to do.
By way of example; The European Communities Act is the UK legislation that gives EU law the force of UK law. If some EU law says "X must not be done", a piece of UK law that says "The Prime Minister must do X" would probably be disapplied. However, Parliament could pass a different piece of UK law that said "The European Communities act is amended to ignore the obligation under EU law that X must not be done, and the Prime Minister must do X". That would (by my understanding), not be subject to such a ruling by the court.
Such a ruling by the courts might be considered to be a ruling of unconstitutionality - I hadn't considered it that way. It seems to me instead to be a matter of the court interpreting exactly what the law is; the Merchant Shipping Act was not intended to contradict EU law, it was, in effect, simply a mistake of drafting that the Court's ruled was ineffectual due to the primacy of EU law. Note that the Act in scope for Factortame was not in effect repealed by the decision; just that the relevant provisions (and not the rest of the Act) were "disapplied", and the Secretary of State barred from taking any action to enforce them:
further order herein the operation of Part II of the
Merchant Shipping Act 1988 and the Merchant Shipping
(Registration of Fishing Vessels) Regulations 1988 be
disapplied and the Secretary of State be restrained from
enforcing the same in respect of any of the applicants and
any vessel now owned (in whole or in part) managed
operated or chartered by any of them so as to enable
registration of any such vessel under the Merchant Shipping
Act 1894 and/or the Sea Fishing Boats (Scotland) Act 1886
to continue in being
However, I am many things, but a constitutional lawyer is not one of them.