How does one become so and what are the implications of it becoming so?
Other answers that explain and further elaborate or reference the concept most welcome but I’ve just seen this (Thoburn v Sunderland City Council, paragraph 62):
In the present state of its maturity the common law has come to recognise that there exist rights which should properly be classified as constitutional or fundamental: see for example such cases as Simms  2 AC 115 per Lord Hoffmann at 131, Pierson v Secretary of State  AC 539, Leech  QB 198, Derbyshire County Council v Times Newspapers Ltd.  AC 534, and Witham  QB 575. And from this a further insight follows. We should recognise a hierarchy of Acts of Parliament: as it were "ordinary" statutes and "constitutional" statutes. The two categories must be distinguished on a principled basis. In my opinion a constitutional statute is one which (a) conditions the legal relationship between citizen and State in some general, overarching manner, or (b) enlarges or diminishes the scope of what we would now regard as fundamental constitutional rights. (a) and (b) are of necessity closely related: it is difficult to think of an instance of (a) that is not also an instance of (b). The special status of constitutional statutes follows the special status of constitutional rights. Examples are the Magna Carta, the Bill of Rights 1689, the Act of Union, the Reform Acts which distributed and enlarged the franchise, the HRA, the Scotland Act 1998 and the Government of Wales Act 1998. The ECA clearly belongs in this family. It incorporated the whole corpus of substantive Community rights and obligations, and gave overriding domestic effect to the judicial and administrative machinery of Community law. It may be there has never been a statute having such profound effects on so many dimensions of our daily lives. The ECA is, by force of the common law, a constitutional statute.