What next? The Union has survived, but its long-term viability now depends on deeper institutional and democratic reinvention. How our political leaders respond to this historic moment will say much about the extent to which they understand the times we are living through.

The first priority is of course Scotland: divisions need to be healed and the country needs to come together. Unionist and nationalist politicians can demonstrate their commitment to such unity by ensuring the smooth transition of the promised new powers to the Scottish parliament, which will require unionist legislation at Westminster and nationalist consent at Holyrood.

Further devolution to Scotland will rightly precipitate calls for a wider reconfiguration of the Union, including most obviously England's place in it. The constitution-making on the hoof of recent days might have helped save the Union but it is no model for the future. What is needed is a process that replicates, as far as is possible, the passionate democratic conversation that the referendum has provoked in Scotland. For sure there have been bitterness and unsavoury aspects to the campaign, but the Scottish electorate has undeniably relished its opportunity to exercise and express its popular sovereignty.

This energy and momentum cannot be allowed to dissipate. It must now be channeled into a process for wider democratic renewal where the people themselves are in the lead. Hence the call from various quarters for some kind of constitutional convention. Certainly it isn't the time for the usual commission of the great and the good to prescribe the future from on high. Nor should we settle for a convention dominated by the political parties and other interest groups (this means going further than the model proposed by Carwyn Jones, the Labour leader of the Welsh assembly). Political parties find it impossible to resist the temptation to succumb to party interests on matters constitutional. Labour's deafening silence on the West Lothian question whenever the subject of England is raised, as with recent Conservative calls for an unrestrained form of 'English votes on English laws', are proof enough that the parties have sectional interests that they cannot easily put aside. It is essential, therefore, to find a mechanism that puts the broader construction of a national interest first.

This does not mean that the political parties should be excluded, however. Just as important as ensuring this is a genuinely open and democratic experience is the need to guard against the rise of a toxic, anti-politics populism. We need a model that complements rather than usurps representative politics.

For guidance we can to turn to Ireland, which established a constitutional convention in the wake of the financial crash and the collapse of trust in politics that crisis precipitated. Politicians were able to participate but not to dominate: two-thirds of its members were Irish citizens selected by lot, with the remainder made up of politicians. To be sure, the agenda was too broad, covering an eclectic mix of political and social issues, and the timetable too tightly drawn. Nevertheless it has produced real change that simply would not have happened without the convention: the government has, for example, accepted the case for a referendum on same-sex marriage. The convention also succeeded in galvanising wider public debate, especially when discussing salient issues. Alan Renwick, the political scientist, has surveyed the different constitutional conventions used across the world and concluded that the Irish model offers the best chance to secure 'public and political legitimacy'.

A constitutional convention along these lines, with a strong element of direct citizen participation, must now be established here. There should be a clear commitment that its proposals will directly feed into the parliamentary process, becoming law if they can command a majority. It should explicitly seek to reach out and engage the wider public, sparking similar sorts of conversations to those we have witnessed in Scotland. It may not match the level of interest in the referendum, where the stakes were obviously higher, but the positive experience of citizens' assemblies in Ireland and Canada suggest they can capture the public imagination and reinvigorate the public sphere.

The precise shape of such a convention will need to be thought through – notably, how best to address the position of the constituent nations, alongside overarching UK-wide matters. There are big issues to be discussed, perhaps the most pressing being those centred on England. Whereas Scotland, Wales and Northern Ireland have had regular initiatives designed to strengthen their devolved institutions, England has been repeatedly ignored. This has to change, and, as the Future of England survey confirms, there is genuine appetite among the English for debating the way they are governed. Options for giving England greater recognition in our constitutional arrangements, both at a national level and via devolving powers within England, all need to be considered. Attention must also be given to what form the cultural representation of Englishness might take.

In Wales there are longstanding concerns about the perceived unfairness of the funding settlement. In Northern Ireland there are calls for stronger tax powers. IPPR's 'Devo more' programme sets out a prospectus for greater self-government (for example, on tax and welfare) within the Union that could work across all the devolved nations.

The momentum therefore is towards a looser Union, one characterised by the further dispersal of power, which raises important questions about how the Union can be made to work in an era of enhanced devolution. Institutional reforms that are federal in nature are needed to ensure effective representation of the home nations, which allow the UK and devolved institutions to pursue shared goals where it is convenient to do so, and crucially to manage the relationship between them. One important rider to all this is that in 2015 the UK government must undertake the most important spending review of recent decades: it is critical that fiscal decisions taken in that review involve major decentralisation of tax and spending powers in England, as well as steps towards a more balanced and fairer UK-wide institutional funding settlement. The Barnett formula will inevitably have to be put back on the negotiating table.

The democratic genie is out of the bottle. These are momentous times. Only a bold response, one which entrusts the people with the opportunity to shape the way in which they are governed, will demonstrate that our political leaders are in tune with the prevailing zeitgeist.