Justice Secretary Jack Straw has sent out a strong signal that the government is ready to draw up Britain's first ever written constitution.
Mr Straw outlined his thinking in Washington DC on Wednesday.
He said the move would encapsulate in one document a citizen's rights, their responsibilities and an outline of how the different arms of government work.
He told the BBC the process could take 20 years and depend on a referendum.
In a speech in the US he said most UK people "struggle to put their finger on where their rights are".
Mr Straw is already working on a new Bill of Rights and Responsibilities, which could be used as the basis of a written constitution.
It would spell out an individual's obligations to society and place a new emphasis on the concept of civic duty.
He concedes that some aspects of a country's constitution should change to reflect the modern world - a remark interpreted as a reference to the difficulties of dealing with terror suspects.
Mr Straw, who oversaw the introduction of the controversial Human Rights Act when he was home secretary, outlined his thoughts in a speech at George Washington University during a three-day visit to the US.
He said the UK could learn a great deal from the US constitutional system "with regard to the enviable notion of civic duty that seems to flow so strongly through American veins".
"It is made much easier to fulfil your civic duty when you have a clear sense of to what you belong and what it is expected from you."
Mr Straw says the constitution of the UK "is in our cultural DNA".
However, "most people might struggle go put their finger on what those rights are or in which texts they are located".
"The next stage in the UK's constitutional development is to look at whether we need better to articulate those rights which are scattered across a whole host of different places and indeed the responsibilities that go with being British."
Mr Straw said developments in the UK had been a "quiet revolution".
The Human Rights Act "was a landmark in the development of rights in the UK", but the question now was "whether this goes far enough", he said.
"We need now to think very carefully about whether a British Bill of Rights and Responsibilities should be a step towards a fully written constitution, which would bring us in line with most progressive democracies around the world.
"But that is a debate for another time."
Earlier he told BBC Radio 4's Today programme that if the government went for a full written constitution, it would take between 10 and 20 years to establish and would involve a referendum.
The existing British constitution is contained in a wide range of written documents - tracing back to Magna Carta in 1215 - and common law.
Liberal Democrat justice spokesman David Heath said: "The Liberal Democrats have long argued for a written constitution, subject to a national referendum.
"If ministers are serious... it should not be drafted behind closed doors by politicians but by a constitutional convention that includes members of the public.
"It is about time ministers trusted people and involved them in decision making, rather than just consulting them."
Professor Robert Hazell, of the University College London constitution unit, said he thought it unlikely that Britain would ever have a written constitution.
"Constitutions don't get written in cold blood.
"Written constitutions typically follow defeat in war, a revolution, independence or the collapse of the previous system of government.
"None of those fates is likely to befall the UK. So however desirable it may be, a written constitution isn't going to happen".
But Professor Hazell said he did support the government's interest in developing a British Bill of Rights.