If the rights of a citizen aren't documented then they don't really have anything that seems permanently binding to make them feel secure that those rights won't just be violated. It would probably help the citizens better understand the rights that they have under the country they live in as well.
If a British citizen does have rights, then what reason is there for not expressly enumerating these rights in a formal document? If rights are coming out of some ethereal ether or from a complex series of common law decisions, then who can understand them or decide whether they have been violated? All civilized nations should enshrine the rights their citizens possess in a legal document which is the law of the land.