Do not assume that a UK/US comparison is valid. Moreover, the UK has no codified (written) constitution -- that is, there is no one single document that IS "The Constitution." Basically, the governance of the UK is based upon two principles: Respect For Law and The Primacy Of Parliament.

The American colonies did NOT want to separate from Britain, but as they wrote in 1776:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, — That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn that mankind are more disposed to suffer, while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security. — Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States.

Whether or not the reasons following are true, they were believed such at the time. Thus later we have statements such as:

"No free man shall ever be debarred the use of arms. The strongest reason for the people to retain the right to keep and bear arms is, as a last resort, to protect themselves against tyranny in government."
       -- Thomas Jefferson, Thomas Jefferson Papers, vol. 1, p.334

"The best we can hope for concerning the people at large is that they be properly armed."
       -- Alexander Hamilton, The Federalist Papers at 184-188

Men trained in arms from their infancy, and animated by the love of liberty, will afford neither a cheap or easy conquest.
    -- From the Declaration of the Continental Congress, July 1775

"To disarm the people... was the best and most effectual way to enslave them."
                        -- George Mason, speech of June 14, 1788

Are we at last brought to such a humiliating and debasing degradation, that we cannot be trusted with arms for our own defence? Where is the difference between having our arms in our own possession and under our own direction, and having them under the management of Congress? If our defence be the *real* object of having those arms, in whose hands can they be trusted with more propriety, or equal safety to us, as in our own hands?
                        -- Patrick Henry, speech of June 9 1788

That the said Constitution shall never be construed to authorize Congress to infringe the just liberty of the press or the rights of conscience; or to prevent the people of the United states who are peaceable citizens from keeping their own arms....
-- Samuel Adams, in "Phila. Independent Gazetteer", August 20, 1789

There are more recent statements, from people such as John Stuart Mill, JFK, Hubert Humphrey, and Mohatmas Gandhi, which I could also quote.

This is for discussion, not polemics.