It is frequently argued that the United Kingdom ought to have a codified ("written-down") constitution. For example, here is an earlier look at this question (post 28 November 2019).
The UK's constitutional arrangements are a product of history and the arrangements have to be divined from a complex mixture of common law, legislation, and practices (or conventions) generally accepted by those who exercise powers within the system. There is no single starting-point document labelled "The Constitution".
In Cherry / Miller 2  UKSC 41, Lady Hale said (para 39) - "Although the United Kingdom does not have a single document entitled "The Constitution", it nevertheless possesses a Constitution, established over the course of our history by common law, statutes, conventions and practice."
That is all very well but, for the majority of citizens, the arrangements are shrouded in mystery rather like the arcane learnings and rituals of some ancient religion.
A codified (or "written") constitution is therefore a beguiling prospect but the idea requires serious examination. There is a great deal of literature on this subject and links to some of it are offered below.
A document would have to be prepared perhaps by a Royal Commission or a Parliamentary conference or by some other method. The public ought to be involved in any process. Having prepared the document it would have to be brought into force and, to ensure general acceptance, that might well require a referendum with a substantial majority in favour in each of the four nations of the UK. In that way, a constitution might be one approved and adopted by the people. I do not say that any of this is impossible but the difficulties are clear. Then it would have to be brought into law by some method that prevented its easy repeal or alteration unless procedures set out in the constitution itself were followed. As things stand, parliamentary sovereignty stands in the way of such an arrangement since a parliament is free to undo what its predecessors have done.
Further problems would arise about the contents. A very short document might achieve very little and a very lengthy detailed document could prove to be far too restrictive. Updating of the document would also be required from time-to-time unless the constitution were to become stuck in the past. The higher judiciary would inevitably become interpreters of the constitution and case law would build as points were decided by the courts - in particular, the Supreme Court of the UK.
Despite such problems, a codified constitution could improve clarity in some areas, could entrench human rights so that they could not be altered by Parliament at the mere suit of the governing party, and a codified constitution could strengthen the position of the devolved legislatures.
Should the siren voices calling for codification be ignored? I am of the view that a better road to take in the shorter term is constitutional reform of -
a) the electoral system - replace first past the post elections with proportional representation - post 15 August 2021,
b) abolition of the House of Lords - to be replaced with a wholly elected second chamber smaller than the Commons - post 16 August 2021
A possible third area of reform would be to require Parliament to normally legislate in accordance with a set of constitutional values - post 18 August 2021.
Without reforms (a) and (b) the UK will not be a modern 21st century democracy and its constitution will be increasingly mired in the past.
Cherry / Miller 2  UKSC 41
Constitution Unit Blog (8 January 2020) simply asked - Do we need a written constitution.
A case for codification is set out at University of Cambridge - Bennett Institute for Public Policy - 4 March 2020 and also at Theos - 25 October 2019.
18 August 2021