Because it is constantly changing and becoming larger, it would cost a lot of money and a lot of time to write down every detail of every law that exists. Even the most narrowly detailed written constitution cannot include every single feature or process of a political system; also, most `unwritten' constitutions include at least some statute law or other written provisions. In either case, according to Graham Maddox, the ``roots of constitutionalism are to be sought in the soil of a community's public and social life". Most people already know the most important parts of the constitution; therefore there wouldn’t be much need to write it down.
There are also arguments that an unwritten constitution is political suicide. If a radical party should come to power they could change the constitution almost any way they like (e.g. Hitler) but a written constitution would stop this problem before it happens. However, Britain is a very strong country and we have not been successfully invaded since 1066 and so there is not much chance of an extremist coming into power easily, or even at all.
A constitution is not just a body of basic law. It is a habit of mind which respects that law. The words of the basic law may be etched in brass, but the habit of mind only lasts if our polity practices it daily. Any constitution, written or unwritten, if it is too often altered, and particularly if it is altered capriciously, weakens.
The main reason for a written constitution is not in order to write down the role of the Crown. It must begin by setting out a country's aspirations. For example, that all citizens should be equal and that they way they are governed should be open, accountable and fair. Its next job is to define the distribution of power, between local, regional and central government and between the executive and the legislature - between who exercises power and who makes the laws. Finally, it must set out the rules for changing the rules.
And it is this function that is the most important of all. In Britain today the government can alter the laws affecting your freedom of speech in the same way it amends laws about dog licensing. A written constitution could protect fundamental rights and democracy better by requiring a special degree of consent from the people (a referendum, say) if laws affecting these rights were changed.
In other words, a written constitution is a way of limiting the power that our system grants to those elected to Downing Street. They are the ones who now enjoy royal prerogative power. The Lord Chancellor, indeed, who is currently 'in charge' of altering the country's constitution more drastically than it has been for three hundred years, has compared himself to Henry VIII's Cardinal Wolsey.