The U.K. Constitution is now almost wholly written in light of decades of law reform in the area, but it's not consolidated into a single document, and is not especially well codified. (See the final paragraph below).
Since 1997 there has been a significant roll-back of the personal prerogative by successive Parliaments legislating in areas where it was routinely exercised. As a recently relevant example, the Lascelles principles (from the Senex letters, for example) became obsolete with the Fixed-term Parliament Act 2011 (which controls events upon the demise of a government by expiration, resignation or loss of confidence), and several recent Representation of the People Acts and some acts controlling secondary legislation such as the Cabinet Manual, which outlines the continuity of government in the event of a demise (death or resignation) of the Prime Minister. The Queen did not have a right to reject Theresa May as Prime Minister even if Cameron's careful announcement of his plan to first tender his resignation and then recommend his successor described the actual order of events; her personal prerogative in the area is obsolete, and the (advised) prerogative vested in Cameron is now strictly controlled by statute.
For better or for worse, what's missing in the UK Constitution is a clear and standard entrenching mechanism. Practically every Constitutional scholar and lawyer in the country would agree that there *is* entrenching, and the concept that one Parliament cannot bind the next has been obsolete as a legal reality for some time, and as a political one for even longer. Ignoring entrenchings coupled to international treaties (e.g. the Single European Act), and entrenchings in the terms of statutes themselves, there are entrenchings controlled by terms in other Acts of Parliament. The tower of legislation needed to remove the Scotland Act would be enormous, for example. And the new Secretary of State for Exiting the European Union and the Attorney-General will be busy for years trying to identify what legislation will need to be included in the effective repeal of the European Communities Act 1972. A misstep will indeed risk the whole enterprise being declared defective by UK courts, which would effectively require Parliament to legislate to correct the defect or outright overrule the ruling (which in turn would need to be done carefully, otherwise "ping pong" results).
In effect, the major difference between Parliamentary supremacy in the UK in 2016 and Constitutional supremacy in Canada or Australia in 2016 is that the Queen of Canada and the Queen of Australia have prerogative powers that are *protected from* the federal parliaments by the Constitution. In the UK, any royal prereogative can be removed by Parliament, and the only protection today is the Queen's Consent (or the Prince's Consent where relevant), which are implemented as standing rules of the House of Commons and subject to change at the will of the majority of MPs. In Canada, for example, an enumerated power of the executive (e.g. the power to appoint Senators where there are vacancies) cannot be removed without the consent of some or all of the provincial legislatures. Several non-enumerated powers have been held by the courts in Canada to require provincial consent too. In the UK, by contrast, the power to summon members of the House of Lords has been modified by Parliament (and in some cases the House of Commons) acting alone several times in the past century, and even in the years since the effective federalism of devolution has arrived as a constitutional reality.
(A clear example is considering the difference between the Fixed-term Parliament Act 2011 in the UK, which withdrew a prerogative power altogether (preventing the executive from dissolving Parliament and calling an election), and the Canada Elections Act 2000 which in establishing fixed election dates had to consider that dissolution cannot be removed without a formal constitutional amendment involving provincial consent, and which preserved the power of dissolution at will by the Governor-in-Council. Likewise, it would take all ten provinces and the federal Parliament to allow Parliaments to operate longer than five years, whereas the UK Parliament could do this unilaterally.)
One can debate whether the lack of a formal standard entrenching mechanism has provided much needed flexibility in the evolution of federalism of the UK (and indeed in participating in the evolution of a federation of which the UK itself has been a member) or whether it will turn out to be a source of bitter and extensive litigation because of lack of clarity over the non-standard and informal entrenchings. (Remember that two of the constituent nations of the UK have their own legal personalities and thus can enter into contracts with the Queen of the United Kingdom through her agents and ministers, and have done so in many areas involving devolved powers and agencies and so forth; it is probable that all the rules of contract-making and treaty-making will apply in the Supreme Court of the United Kingdom, including the entering into enforceable verbal agreements (where English and Scots law diverge, possibly relevantly even... yikes! So it's possible that undoing the Scotland Act unilaterally would be forbidden by the courts unless preceded by general legislation adjusting the law of contracts. And it's hard to imagine how that would not be a recipe for either marketplace chaos or damaging the UK's attempts to form trade and other agreements with other countries in implementing Brexit.)
Finally, there have been references to the Supreme Court of Canada (and a couple of other Commonweath courts have had similar cases) seeking to define what outside the central document is part of the constitution and thus subject to its entrenching formulae. There has not *YET* been a case to the Supreme Court of the United Kingdom or its predecessors that produced a similar list, however, it seems clear that the Scottish executive and possibly the executive of Northern Ireland are likely to cause that to happen in due course in light of "Brexit Means Brexit". The list is likely to strongly resemble the Canadian one, and you can bet that the parties will quote from the (persuasive) sources that determined the list. https://www.wikiwand.com/en/Li...