In the UK, all laws formally require the Monarch's consent. This is very much a formality, and in practice the modern Monarch would never fail to grant consent to passed legislation, but technically speaking it's possible for the Monarch to refuse consent for whatever which reasons, including it being "unconstitutional". This is probably a common feature of many existing Constitutional Monarchies, though I haven't delved into them to know which for sure do.
But the supreme sovereign authority in the UK is Parliament. They can strip the Monarch of whatever which powers they so desire, or otherwise modify them; or add powers even, though I don't think that's happened in a very long time. Similarly, Parliament can also overrule any court ruling by simply passing a law to that effect.
As a subcase, the House of Lords, the upper chamber of the Parliament, ostensibly has its primary function to be reviewing new legislation for conflicts with existing legislation and "constitutionality". Before the creation of the UK Supreme Court, it was in fact the explicit power of the House of Lords to serve as a sort of "Supreme Court". Though keep in mind that there is no single written Constitution in the UK. It is rather the abstract corpus of all traditions, laws, and treaties. But this is otherwise, in some sense, a power of the sort you desire.
As before, if the Lords declare a given piece of legislation problematic, the Commons can simply override that declaration and pass the legislation anyway (in practice they usually try to amend the law in question to avoid or eliminate the issues, or make it clear which of itself or existing laws is to take precedence when in conflict). They could even go so far as to alter the Lords and their powers, or eliminate the upper chamber entirely.