UK operates on the notion of parliamentary supremacy, which makes any constitution, formal or informal, largely meaningless, since the Parliament can always override anything in it with simple majority vote:

"It is often said that it would be unconstitutional for the United Kingdom Parliament to do certain things, meaning that the moral, political and other reasons against doing them are so strong that most people would regard it as highly improper if Parliament did these things. But that does not mean that it is beyond the power of Parliament to do such things. If Parliament chose to do any of them, the courts would not hold the Act of Parliament invalid."