There seems to be an odd misperception that the UK doesn't have a constitution guaranteeing individual rights. Just to clear this up, the UK does have a constitution and it does guarantee most of the same right that US citizens enjoy, but it isn't embodied in a single document and it can be modified by parliament. When discussing a 'UK Bill of Rights' recently, David Cameron was actually contrasting this with our most recent legislation on the subject, the Human Rights Act of 2000 (I think it was), which simply put the European Convention on Human Rights into UK statute law and which has arguably restricted the ability of the UK parliament to make law.
All good Americans should remember that one of the reasons for the American revolution was that the British government didn't allow the protections of the 1689 Bill of Rights to be extended to the colonies!