The absence of a written constitution is one of the factors that made it possible for Tony "The Terrorist" Blair (see my article here on the Chilcot's Cheating Us blog for the background) to take the United Kingdom into an unlawful war in Iraq.
The absence of a written constitution makes it possible for governments and others in positions of power to make up the rules as they go along.
If the rules aren't clear it encourages abuse of power without any proper checks and balances to rein in such abuses.
Party politicians in positions of power will oppose real accountability. The feeble accountability of a General Election needs to be bolstered by a legally enforceable written constitution.
Serious transgressions by politicians, including Government ministers, should be open to investigation by the Police and to trial in open court.
In fact, a worthwhile written constitution should impose a duty on the Police to investigate prima facie evidence of wrongdoing by politicians or senior civil servants.