Britain has a constitution, although it is a looser one than the US.
http://en.wikipedia.org/wiki/British_Constitution
Britain has only traditions and laws, and the concept of Parliamentary Supremacy. In countries with Parliamentary Supremacy, there is not -- nor can there ever be -- a Constitution, because there is no power above the legislature. Rights Englishmen have enjoyed since Magna Carta can be swept away by nothing more than a majority vote.
Witness, for example, the English Bill of Rights (containing a few, very immature, ideas about ordered liberty.) That so called "Bill of Rights" contains a provision for the right to keep and bear arms. That provision was long ago destroyed in all meaningful senses by acts of Parliament.