There are times in a country's affairs when it has to think big. The next 10 days are such a time. Without imaginative and creative statecraft, the polls now suggest Scotland could secede from a 300-year union, sundering genuine bonds of love, splitting families and wrenching all the interconnectedness forged from our shared history.

Absurdly, there will be two countries on the same small island that have so much in common. If Britain can't find a way of sticking together, it is the death of the liberal enlightenment before the atavistic forces of nationalism and ethnicity – a dark omen for the 21st century. Britain will cease as an idea. We will all be diminished.

Yet there is no doubting the energy and optimism of Scotland's yes campaigners. What is happening goes well beyond a grab for oil or arguments about whether independence will make Scots a thousand pounds better or worse off.

The big argument is that Scotland does not need to be permanently yoked to English Toryism's infatuation with a libertarianism that denies obligations to society and each other, has abandoned justice and equity in its public policy positions and is the author of the great "cashing out" of the past 30 years. All our utilities, five million council houses, many of our great companies and swaths of real estate in our cities have been cashed out in the name of market forces, of liberalisation, of being open for business and wealth generation. What has been created is predator capitalism, massive inequality and a society organised to benefit the top 1%. The country needs to build, innovate and reinvent social partnership. Independent Scotland can strike out in this direction.

Yet as proposed by the nationalists, it is not a very different direction – rather a series of compromises designed to persuade voters that they can keep what they like while discarding what they don't. In reality, this semi-independent Scotland, using the pound but submitting to tough rules about taxing and spending so that England could ensure it was not being exploited, would trap Scotland in an uneasy dependence. It would be quasi-federalism but with none of the advantages.

The only offer that can now persuade Scotland not to secede is to trump that half-cock quasi-federalism with a proper version. Westminster's party leaders must offer to create a federal Britain and irrevocably commit to a constitutional convention to discuss its implementation if Scotland votes no.

This is not "devo max", or further incremental powers to control social security or taxation. This has to be the real deal – a wholesale recasting of the British state so that Scotland, Wales, Northern Ireland and all Britain's great cities and towns have the autonomy they need to create the societies and culture they want but within the protective umbrella of Great Britain. This really would be the best of both worlds, and not just for Scotland.

The first casualty would be the Treasury, which would lose its powers to set spending, taxes and borrowing for the constituent parts of federal Britain. It would be little mourned, – an institution dedicated to "controlling" the rest of government in its uncreative iron grip and personifying the investment-aversion that informs the British state. Instead it would become a humbler finance ministry. The next casualty would be the House of Lords. Federal Britain, like the federal US and Germany, would need a second chamber that represents all parts of the federation. The House of Lords would become the House of Britain. The elected assemblies in Scotland, Wales and Northern Ireland would be in control of the whole spectrum of domestic public activity, with a freshly created English assembly joining them. Cities and towns would be afforded the same autonomy, within broad indicative guidelines set by elected national politicians in the now smaller House of Commons.

Gordon Brown is asking for a two-day parliamentary debate on devolution after the referendum: it is a step in the right direction, but hardly rises to the scale of the risk. Only a commitment to a fully fledged constitutional convention to discuss how to federalise Britain will now stop the yes campaign in Scotland. The whole country could be energised – and Scotland, in forcing these long overdue reforms, will have done everyone a huge favour.