Purpose of a constitution... a framework of rules which dictate the relationships between people and the state and how the state should govern. Perhaps consider Locke's thory of Natural Rights - the social compact - the notion that people surrender liberty in exchange for protection whilst reserving the right to "revolt" and replace that government should they fail to deliver what the people want. The purpose, therefore, of the constitution is to provide a set of rules that defines the relatiosnhip between all parties.
Strengths of the UK Constitution - Flexible, can be changed QUICKLY (by a simple statute as opposed to time-consuming development through the common law. By the same token it will be/should be relatively "precise" in its terms (unlike the US cosntitution which relies on interpretation of "oiginal intent").
Weakness - Parliament is supreme - however, where are the checks and balnces; the seperation of powers? Consider the role of the Lord Chancellor - Head of the judiciary, a memeber of the executive and, as a cabinet minister a member of the legislature... Consider the role of the Law Lords - High ranking memebrs of the judiciary and members of the legislature (although by CONVENTION - though not by law - they do not as of a rule get involved in the legislative process). And that takes me to another weakness - CONVENTION - much of the Uk consitituion relies on conventions - acts (or people omitting to act - e.g. Royal prerogative) which are not recognised in law. The conventions can be broken - often many times - but they will rmeain "convnetions" until the acto fo breaking them enough times develops the "new" convention - again, not recognised in law.
just a few things off the top of my head...