Saying that, a well written constitution that is abided by can protect quite a lot, for instance the German Basic Law (written largely by the British and only originally meant to be temporary) is an example of a constitution that has worked well without hardly any alteration- the same constitution here for example would have prevented Thatcher abolishing effective local government in the 1980's and also prevented the Tories introducing the Poll tax, it would also have made it a lot more difficult for any government to take us to war. The advantage those drawing up the German Basic Law had, was that they could (after the disaster of Nazism) start from scratch and as outsiders were not overly concerned with any strange local traditions or vested interests. So any constitution usually depends on the starting position we find ourselves in. In this respect the UK has some tidying up to do (not least its undemocratic dysfunctioning electoral system).
Yes, some rights have been eroded since 2001 by this government (The hysteria following 9/11 and our right wing press have put exceptional pressure on the government to 'act tough' - this is pressure they have sadly caved in to) but this government have still restored more rights than they have taken away (Those who talk of a police state and Nazism really insult those who have to live under such things and frankly devalue the power of such words to a ludicrous degree - they really are quite pathetically ill informed). The Tories would have laughed at the idea of a transparent register of party donations, reform of the House of Lords, the Freedom of Information Bill, gay rights, non-smokers rights, maternity and paternity entitlements, guaranteed paid holidays, devolution, signing up to the Social Chapter and the Human Rights Act.
Those who talk about 28 days detention and minor restrictions on impractical large scale or long-term demos outside parliament (demos are still allowed outside parliament by the way) forget the Tories had the sus law, internment and a ludicrous counter-productive ban on Sinn Fein speakers in the media that made us a laughing stock of the world (the nice actor voices improved Gerry Adams image no end).
Most of the problems with rights in this country Labour have inherited from the previous Tory administration and failed to reverse. It was the Tories who introduced unaccountable quangos, showed contempt for parliament by guillotining bills through without proper debate - far more than Labour ever dare (Thatcher/ Major also had the Tory House of Lords onside who waved through the Poll Tax and abolishing local government without a murmor. Labour have had to fight like crazy against the unelected Lords for gay rights and other equalities legislation. Under the Tories the only thing the House of Lords rebelled against was when they fought tooth and nail to defend elderly Nazis from prosecution - shows how out of touch they are). The Tories also set in train the wasted millions on management consultants in the NHS and the idea to make the Dome a temporary structure which caused so much trouble, they emasculated local government and over-centralised everything in Whitehall. Gordon Brown will have to right a lot of these Tory wrongs before we could have a decent written constitution (including electoral reform to make sure we have a government in the first place that the majority want).
The basic justification for a written constitution is that there are certain inalienable universal rights that should never (or without unbelievably good justification) be over-ridden. Most countries in the world agree that this concept is sound - very few countries are like the UK with a confused mess of laws and tradition that can easily be changed (By the way those who talk of the Magna Carta in exulted terms are really quite laughable and have probably never read the thing - it was great for its day but hopelessly outdated now). This is supposed to act as our 'unwritten constitution' - this protects no-one (of course it wouldn't be quite so dangerous if we didn't have an electoral system that allows a party to govern with just 35% of the vote and 22% of the registered electorate on a very poor turnout (or possibly much less support than this in the near future).
So my basic point is - yes to a written constitution but only if it is as good as the German Basic Law and we decentralise power (including tax raising powers) and change to a proportional electoral system for all our parliament- otherwise it is just window dressing.