Willliam Hague is being urged to set up a special citizen-led convention with "real powers to decide the future shape of the UK".
A group of 28 experts, academics and others have written to the leader of the House of Commons, arguing that members of the public should be given the lead when it comes to determining the constitutional future of the UK.
They are calling for a constitutional convention to be set up, featuring people from England, Scotland, Wales and Northern Ireland, and propose that a majority of its members be "randomly selected from the population in a way which represents the UK as a whole".
The group told Mr Hague - who has been tasked with chairing a new cabinet committee looking at devolved powers for England, Wales and Northern Ireland alongside further devolution for Holyrood - that "a citizen-led constitutional convention is the only way to answer questions about the future of the UK in a way which commands legitimacy and ensures a sustainable settlement".
They insisted that "it will not do for politicians to make these decisions about our constitutional future behind closed doors".
The group continued: "In a time of low election turnouts and rising distrust in politicians, it is essential that people are given a say in the shape of our political system."
Electoral Reform Society chief executive Katie Ghose is one of those who have signed the letter, along with Professor Vernon Bogdanor, an expert on constitutional politics from Kings College London, and Graham Allen, the chair of the House of Commons Political and Constitutional Reform Committee.
Other signatories include Professor Patrick Dunleavy, the co-director of the group Democratic Audit, and Sir Stuart Etherington, the chief executive of the National Council for Voluntary Organisations.
The group said they represented "a broad range of civil society - including democracy experts, membership organisations and academics".
The convention they want to see established would focus its work on deciding the balance of power between Westminster and the nations and regions of the UK, with mechanisms in place, including the use of referendums, for ensuring its recommendations are acted upon.
The constitutional future of the UK is being considered in light of last month's Scottish independence referendum, which resulted in a vote to remain in the union.
Substantial new powers were promised to Scotland by the leaders of the three main parties in the run up to that vote, leading to calls from some for only English MPs to be allowed to vote on English legislation.
The group said: "When it comes to new Scottish powers, there is clearly no going back on 'The Vow'.
"But once these powers are delivered, there will still be wider questions about where power should lie elsewhere within the United Kingdom. Your committee is tasked with answering these difficult questions. We believe the best way of approaching this task is to give the lead to citizens, within a clearly defined process of decision-making."
They said the referendum, with its record 85% turnout, "demonstrated people's enthusiasm for making decisions about the future of the UK", adding: "When given a real choice with real influence, Scots turned out to discuss, debate and vote on their future in unprecedented numbers.
"We urge your committee to build on this passion and give people across the UK a role in shaping the country.
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