Leanne Wood is rather different from most of the UK's politicians. Forty years old and a mother of one, she still lives in the same street in the Rhondda Valley where she was born and brought up. She thinks the crash of 2008 should have "resulted in the rejection of capitalism and many of its basic economic and political assumptions", and that the UK's coalition amounts to a "hyper-competitive, imperial/militaristic, climate-change-ignoring and privatising government". She is also a proud republican, who refuses to attend the kind of official events at which the Queen turns up, and was once thrown out of the Welsh assembly for referring to the reigning monarch as "Mrs Windsor". If any of this chimes with your general view of what's wrong with the world, it's fair to say that you'd like her.

If Wood pursued her political career in Westminster, her opinions might ensure she was kept safely on the fringes. But in her home country, she is a high-profile voice – and the current favourite to take over the leadership of Plaid Cymru, the nationalist party who, until 2011, shared power in Wales with Labour. With the result due on 15 March, Paddy Power has 4-5 odds on to win; in her Cardiff office, there is a sense of quiet expectancy.

The prospect of life as party leader is not the only reason for her air of energised enthusiasm. Being a senior Plaid Cymru figure, Wood believes in Welsh independence. And with Scotland set to vote on whether to stay part of the UK in 2014 and the future of the union being argued over as never before, Wood and her fellow Welsh nationalists think there is an unprecedented opening for the most fundamental of their beliefs. Certainly, if Scotland makes the leap and leaves a rump United Kingdom of England, Wales and Northern Ireland ("Little Britain", as it's recently become known), Wales's marginal position will be self-evident: it will have 30 Westminster MPs to England's 502, and bump against the political and economic dominance of the English south-east as never before. With that grim prospect on the horizon, Wood thinks these could be fertile times for her and her party.

Membership of Plaid has gone up 23% in the past four months. And while its senior politicians once held that pointed talk about independence was a vote-loser, all four of the current leadership candidates are falling over themselves to underline their vision of a Wales finally free from the English yoke.

Leanne Wood, one of four candidates in the running for the leadership of Plaid Cymru. Photograph: David Levene for the Guardian

"Before," Wood explains, "the question of independence was a bit of an anorak issue. But now it's in the mainstream: it isn't something that's such an impossible dream. It's now tangible for Wales: we're in a position to be able to start talking about independence in a normalised way. There's still a lot of debate to be had: I think they're further ahead than us in Scotland. But I think now is a good time for the debate, because of what's happening with the economic crisis. People are being squeezed, and the future looks pretty grim. I'm sensing that people are looking for an alternative solution. And I think that independence is potentially it."

So she thinks these are exciting times? "Yeah, yeah. Everything's up for grabs, isn't it?"

As if to underline the idea that politics in Wales defies the staid norms of Westminster, both front-runners in the Plaid leadership contest are women. Wood's closest rival is 45-year-old Elin Jones from west Wales, whose odds of winning are currently put at evens. She is a much more strait-laced presence, but is equally convinced that the next few years could jump-start the case for Welsh independence. "If Scotland becomes an independent country, the UK ceases to exist," she tells me. "You get a combination of England, Wales and Northern Ireland. Now, is that a country? Well, no, it's definitely not a country. Is it a state? It's so imbalanced that you couldn't make it up if you were starting from scratch. All that calls into question a huge number of issues about the future of what might be left, post-2014.

"I've said quite clearly that over the next 12 months I want to see us define a route map for independence in Wales," she says. "Two consecutive Plaid Cymru victories in an election could trigger an independence referendum. That could happen as early as 2020."

This, undoubtedly, is over-excited talk – but if you buy the idea that the UK is fracturing, and that Alex Salmond's success may not represent the only proof, there is still a specific Welsh story to tell. It may not point to independence – nor, given that large swaths of Wales remain firmly dominated by Labour, mean any huge advance for Plaid Cymru. But it says a lot about the increasingly separate journeys taken by Wales, Scotland and England, and the hugely uncertain future the UK now faces.

Not that many English people have been paying much attention, but since the late 1990s, devolution has inevitably created a specific and self-contained Welsh politics. Last year, a referendum granted the Welsh government full law-making powers in 20 fundamental areas, from health to transport, and an official commission is now looking at extending devolution yet further. On arriving here, you only need glance at the Western Mail to get an instant sense of a different reality: on the day I visit, the front page is taken up by stories about the Cardiff-produced Doctor Who, and the Welsh soccer star Craig Bellamy, along with the injured rugby internationals Dan Lydiate, Gethin Jenkins and Rhys Priestland, and Welsh first minister Carwyn Jones's latest attack on the coalition in London. "Dragging Wales to edge of double-dip recession," says the splash. "First minister hits out at UK government."

Big policy differences between Cardiff and Westminster extend into the distance. There are no Sats tests in Welsh schools, and until they are seven, children in primary education follow a "foundation phase" based on ideas from Finland and Italy, and built around "play and active involvement rather than completing exercises in books". Prescriptions are free, and the Welsh NHS will be unaffected by Andrew Lansley's market-based revolution. When the coalition in London raised tuition fees to £9,000, the government in Cardiff guaranteed to meet the cost of the increase for any student who lives in Wales. As with Scotland, there is a sharp sense of a shared politics well to the left of what prevails in England: I lived in Wales between 2004 and 2009, and though its brand of Celtic social democracy is far from perfect, there's a palpable sense of a society run along kinder, more communitarian ideas than those that hold sway to the east.

Carwyn Jones, first minister of Wales. Photograph: David Levene for the Guardian

That said, drawing comparisons between Wales and Scotland is something of a fool's game. With no separate legal system, nor any latent memory of self-government, the politics of Welsh nationhood is in its infancy. Partly because of its traditionally symbiotic relationship with campaigning on the Welsh language, support for independence here has always hovered at around 10%, and found little echo in the post-industrial, English-speaking south-east of the country, by far Wales's most populous region. There is a strong case for the idea that Plaid Cymru is getting rather ahead of itself: at last year's elections for the Welsh assembly, it came third, behind the Tories, on a not exactly earth-shaking 19% of the main vote.

But still, the path Wales has taken since devolution has led to completely virgin territory: and to hear some people talk, that means that no outcome – including independence – should necessarily be ruled out.

"It's now possible for Welsh people to think of themselves as genuine citizens of Wales," says John Osmond, the director of Cardiff thinktank the Institute of Welsh Affairs. "Don't get me wrong: Welsh people have always felt their Welshness intensely. But until this generation, they felt it in ways that prevented them having any sense of unity around the idea of Wales. They felt their Welshness very strongly in terms of language – but that divided them, because it depended on whether you spoke it. They felt it in terms of a strong sense of place – but that didn't mean Wales, it meant specifically where you're from, which again was divisive. But a civic identity is something people share equally. That's what Scots have always had, whereas the Welsh have never had it until now. People have a new sense of what it is to be Welsh ... And, on the whole, they like it."

Carwyn Jones – who, let us not forget, is the Labour party's most powerful British politician – could probably walk around any English town or city unrecognised. But as first minister, he has a crucial role to play in any conversation about how the UK might be remodelled, with or without Scotland. In response to Alex Salmond's manouevres, he has recently been out on the prowl himself, thinking aloud about what Scottish independence might mean for his country, and suggesting radical changes to the way that Britain's institutions work. On this score, Welsh Labour politicians have tended to think a bit more creatively than many of their Scottish counterparts: here, nationalism, at least with a small "n", runs much wider than the official nationalist party.

I meet Jones in his gleamingly modern suite of offices in the Welsh assembly building. He offers the obligatory statement of support for the UK – "I sincerely hope Scotland doesn't become independent" – and then gets to work, setting out what would happen if Scotland went its own way.

"You'd then have England, Wales and Northern Ireland," he says, "and you couldn't just carry on with the structure as it is now. Potentially, you'd have 550 MPs, more than 500 of whom would be from England. That clearly doesn't work. So there'd need to be a rethink about the nature of the relationship of the three nations." Already, he has suggested replacing the House of Lords with a chamber split evenly between the UK's constituent countries. "You'd have a lower house selected on population and an upper house selected on geography, so there's equal representation. That's something we could look at now. The US does exactly that, and the US is stable.

"All this is not without its complications," he counsels. "It would need a written constitution, there's no question about that. But I do think we're heading towards that situation, in order for the UK to work properly in the 21st century and beyond, and for the people of Scotland to feel that they're fully part of the UK. The reality is, if we want the UK to stay together, can we afford to have a constitutional structure based on the 19th century as we go into the 21st century?"

Does he accept that the Scots leaving would inevitably increase support for Welsh independence?

"Not necessarily, because the first questions people ask are: 'Can we afford it? Is this in our financial interests?' And it's not. The reality is that we spend more than we raise in tax, so there is a subsidy element of money that comes from the south-east of England – not just to Wales, but to, say, the north-east of England. Financially, there's no advantage to it."

This reminds me a little of the essentially pessimistic approach that Scottish Labour politicians took to the rise and rise of Alex Salmond, only to see themselves ruined by one of politics' most underrated rules: that it's the optimists who win. Is it a good enough argument?

"I think it is. What people are concerned about now is jobs, security, houses, opportunities for young people. And the view of by far the largest chunk of the people of Wales is that in terms of the economy, independence would make things far worse."

For anyone who wants to make the serious case for Welsh independence, this is a major obstacle to get over. Of the Welsh workforce, 27.5% is employed by the public sector, and according to some estimates, government spending accounts for as much as 70% of Wales's national income. In short, as Jones says, far more is spent by the state in Wales than is raised in tax – and in the absence of assets as handsome as North Sea oil and gas, the case for independence contains a gaping hole. You need only drive around the classically post-industrial expanses of south Wales – where the economy seems split between the state and big chain stores – to grasp the deep problems that afflict them, and how difficult any plan for economic revival would be.

Wood has her own answer, arguing that Wales has long suffered from being "on the periphery of an economy that is mainly focused on London and the south-east of England and which overheats, to the detriment of the peripheral areas". In her campaign material, she cites claims that "Wales's economic development is typical of other colonial/extractive economies like those in Latin America". Some of her ideas about creating a new Welsh economy are condensed in a document she calls a "Greenprint" for her native south Wales valleys, which draws on examples set by the Basque region and the Danish island of Samso, and sets out a vision of "food sovereignty" and "self-sufficiency". In its sheer audacity, it's certainly breathtaking. But getting anywhere near it would involve a lot of short-to-medium-term hardship, wouldn't it?

"But we're enduring the hardship now, aren't we?" she counters. "Because there are so many people employed in the public sector in Wales, we're already taking a bigger hit from austerity. And if that continues – and I can't see any light at the end of the tunnel, any sign that the Tories' measures are turning the situation round – things are going to get worse and worse, and there are going to be big gaps opening up in the welfare state. So a plan like this is really the only chance we've got."

Back on the English side of the border, I put in a call to Cardiff University's Richard Wyn Jones, an expert on the Welsh political scene, whose most recent work is a pored-over report focusing on rising resentment over post-devolution tensions among a group of people much overlooked in the noise about the UK's future: the English.

"What all this might mean for England is the ultimate issue for Wales," he tells me, before we return to so-called Little Britain, and the scenario of a hacked-down United Kingdom of England, Wales and Northern Ireland.

"What's in Little Britain for England?" he asks. "Northern Ireland is a problem and a financial drain; Wales may not be a problem, but it's a financial drain as well. It might get to, 'Why do we subsidise the Welsh and the Northern Irish? All they do is complain – what do we get out of it?' There's a big question about what that could mean for public spending, and the willingness for transfer money, and all those kind of issues.

"I'm not a prophet," he tells me, "but clearly, it might be very, very difficult." What he says points not to some shining new Welsh dawn, but a much more troubling prospect: turbulence and strife, with no clear resolution. As the song goes, hanging on in quiet desperation is the English way – but it could be the future of Wales, too.