In the years before the 2008 financial crisis, it was sometimes said that Labour’s David Miliband, the Conservatives’ David Cameron and the Liberal Democrats’ Nick Clegg could plausibly belong to the same party. All shared a metropolitan world-view and commitment to economic and social liberalism, and to traditional foreign and defence policy. Though differences endured (such as on EU integration), what united them was more important than what divided them. Those who stood outside this consensus – the Labour left and the Tory right – were derided as irrelevant and outmoded.

The new Independent Group, consisting of eight former Labour MPs and three former Conservatives, is many things: a vehicle to oppose Brexit and socialism, an expression of solidarity with a Jewish MP (Luciana Berger) against anti-Semitism, and a Burkean assertion of the primacy of “representatives” over party delegates. But perhaps above all, it is an attempt to revive the UK’s dormant centre after multiple humiliations, including Jeremy Corbyn’s landslide leadership victories, the 2016 Leave vote and the Liberal Democrats’ electoral routs.

The Independent Group offers a glimpse of what a Miliband-Cameron-Clegg party could have looked like. One is reminded of Tony Benn’s acid observation after the Social Democratic Party’s creation in 1981: “Britain has had SDP governments for the past 25 years.”

In January that year, four former Labour cabinet ministers (Roy Jenkins, David Owen, Bill Rodgers and Shirley Williams) announced their intention to leave the party to form a new organisation, the Council for Social Democracy. In common with the Independent Group, they denounced Labour’s European policy under Michael Foot (automatic withdrawal from the European Economic Community) and the party’s “drift towards extremism” under the influence of the Bennite left.

The Social Democratic Party, which was subsequently founded on 26 March 1981, polled as high as 50 per cent in alliance with the Liberals, attracting 28 former Labour MPs and one former Conservative. It aspired permanently to realign British politics. “The time is ripe for another breaking of the mould, however painful, and even if many people would prefer it not to happen,” declared Rodgers. Or, as the Liberal leader David Steel triumphantly told his party’s 1981 conference: “Go back to your constituencies and prepare for government!”

Today, the party is most often recalled as a failure. The SDP-Liberal Alliance won 25.4 per cent of the vote at the 1983 general election (close to Labour’s 27.6 per cent), but the merciless first-past-the-post system meant only 23 MPs were returned (a mere six of whom were SDP members). “They should have stayed within and fought their way through,” Margaret Thatcher remarked of the Gang of Four in June 1983. “The Labour Party won’t die, the Labour Party will never die. They should have fought.”

Not since 1924, when Labour first formed a minority government, buttressed by an ascendent working class, has a new party taken power alone.

Others, however, believe that the SDP was an unappreciated success. Although it did not break the Labour-Conservative duopoly, it pushed the former rightwards, leading to the creation of New Labour (a name the SDP considered) and its three successive general election victories.

In the years since, other small parties have demonstrated that one need not hold office to wield power. Ukip never had more than two MPs (both Conservative defectors) but its existence helped persuade Cameron to promise an EU referendum. In the House of Commons today, the Democratic Unionist Party, with just ten MPs, derives tribute and influence by propping up Theresa May’s government. Only a week after its creation, the Independent Group can reasonably take credit for forcing Corbyn’s Labour to endorse the possibility of a second Brexit referendum.

The new group both reflects and reinforces an age of political volatility: since 2010, Clegg’s Liberal Democrats, Ukip, the SNP, the Green Party, the Scottish Conservatives and Corbyn’s Labour have all successively surged. Though the two main parties won 82.4 per cent of the vote at the 2017 general election, their highest joint share since 1970, opinion polls resemble an unpopularity contest. Corbyn’s net satisfaction rating stands at -55, the government’s at -49.

But in this era of discontent, what does the Independent Group want? And what would success look like?

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In 25 February, a week after the Independent Group’s creation, I met Chuka Umunna, its best-known MP and presumptive leader, in his parliamentary office. “Frankly, we just wanted to still be standing after the first week, to be considered credible and viable and, my gosh, we’ve surpassed all expectations on that front,” Umunna, the MP for Streatham and former shadow business secretary, told me.

“We did not expect to be received in the way that we have. So it’s taken us all by surprise, we’ve had thousands of emails from all over the country. People stopping us in the street and being incredibly positive about what we’ve done, even if they’re not totally sold on the need for a new party.”

For now, the group’s lack of definition and policy is a political virtue. Voters are able to project any number of wishes on to it (early opinion polls have put public support for the notional party at between 6 and 18 per cent). In some respects, the group is reminiscent of the alliance of independents some predicted would emerge after the 2009 MPs’ expenses scandal; a loose band united by revulsion at “the old politics”.

The Council for Social Democracy, by contrast, was framed in more explicitly ideological terms – it was an unambiguously centre-left group. “Our intention is to rally all those who are committed to the values, principles and policies of social democracy,” the group declared. “We do not believe in the politics of an inert centre merely representing the lowest common denominator between two extremes.”

I asked Umunna whether the Independent Group stood for anything more than an “inert centre”. He replied: “What distinguishes this project from previous attempts to refashion British politics is that this is a group of politicians who share the same progressive values but hail from different political traditions, namely the centre-left, social democratic tradition, the long-standing liberal tradition and the One Nation Conservative tradition.

“The SDP was essentially Labour 2.0: it was primarily social democratic, Croslandite in its complexion. This is different because it has people from other traditions. What is very clear from polling is that people genuinely want something new. They don’t want Labour 3.0 and they don’t want a version of the Liberal Democrats. They want something that is genuinely new.”

Umunna, in terms reminiscent of the sociologist Anthony Giddens’s “Third Way” (one of the predominant influences on New Labour), aspires to transcend the politics of left and right – the categories that have defined debate since the French Revolution.

“We’ve got a good chance of moving towards less of a left-right dichotomy and less of a politics based on class and ownership, and more of one that is principally made up of a populist offering, which could be of the left or the right – there’s often not much between them on a number of issues.”

He cited Future Politics: Living Together in a World Transformed by Tech, by the author and barrister Jamie Susskind. “His basic proposition is that whereas politics previously revolved around a debate on the extent to which the state or the market should control your life, that is not really engaging with the big problems that we have now.

“For example, how are we going to ensure the new digital platforms and technology are a force for good, not a force for bad? There are some aspects of that which you would say are more left-wing, such as ensuring that ownership of these new platforms isn’t just concentrated in the hands of a small number of people.

“On the other hand, you also want to make sure there’s very vigorous competition, a rigorous and efficient free market. You could say that’s a bit more of a right-wing thing. The big difference with our politics is that it’s not about splitting the difference and going for the middle option.”

Like Tony Blair, whom he admires, Umunna would say that “what matters is what works”. But this does not preclude disagreement on what does, in fact, work.

After the longest period of peacetime wage stagnation since the Napoleonic Wars, voters in the UK and elsewhere have embraced policies long dismissed as “unworkable” and unfeasibly “radical”. A YouGov poll published earlier this year found popular support for renationalising the UK’s water and energy industries (57 per cent) and the railways (60 per cent), increasing tax on the top 5 per cent of earners (68 per cent) and abolishing university tuition fees (55 per cent).

When I recently interviewed Umunna’s fellow Labour defector Chris Leslie, he dismissed many of these policies, remarking of renationalisation: “It speaks to the controlling instinct of the hard left… The problem with the Marxist ideology is that it assumes this omniscience on behalf of the central controller.” Of the abolition of tuition fees, he said: “Sounds great. The minor problem is: how do you pay for it?”

Umunna was more guarded: “It would be incredibly unwise to set out a policy programme. The status quo parties would love for us to set out details. We’re not going to do that at this point.”

Pollsters contend that the “unfilled space” in British politics is not for the liberal centrism associated with Umunna and his fellow defectors but for left conservatism. A YouGov survey last year on the “most fertile ground for a new party” found that the views deemed most unrepresented included “the justice system is not harsh enough” (24 per cent), “immigration restrictions should be tighter” (16 per cent), “Britain should not militarily intervene in other countries” (13 per cent) and “government should regulate big business more” (12 per cent).

Umunna, notably, did not reject this analysis. “Blue Labour or Red Conservative, I think there would be a lot in our politics and values that they would identify with. We’re strong on defence but, equally, we want a progressive taxation system – well, those are my personal views, so let me not ascribe these to the rest of the group.

“I’m personally pretty strong and hawkish when it comes to defence matters. I didn’t go into politics to tax people and punish the successful, but I think you’ve got to have a progressive taxation system to properly fund public services.”

Once again, one is unavoidably reminded of New Labour. Though now often described as uncomplicatedly “liberal”, the project also encompassed a more communitarian philosophy and policies such as ID cards, anti-social behaviour orders and, most fatefully, military intervention. Should “strong on defence” merely mean denouncing Vladimir Putin more forcefully, there are few votes to be lost. But should it signal a willingness to intervene abroad, opinion will be more polarised (a mere 27 per cent of voters now support “military interventions in other countries”).

Umunna was dismissive of the notion that he and the other ten Independent Group MPs should trigger by-elections and allow their constituents to pass early judgement: “It’s the Labour Party that’s broken its contract with constituents, not me.”

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The Limehouse Declaration, the 1981 statement that announced the creation of the Council for Social Democracy, was named after the east London home of the former Labour foreign secretary David Owen (one of the Gang of Four). On the evening of 25 February, I visited Owen at the large terraced house he still occupies on Narrow Street, adjacent to the Grapes, the pub part-owned by the actor Ian McKellen.

Owen, who is now 80 and sits as an “independent social democrat” in the House of Lords, expressed admiration for the group’s tactical nous. “It’s been quite clever to call it an Independent Group, that was wise… They are learning from some of the mistakes we [the SDP] made, one of which – a huge mistake – was to ally ourselves with the Liberals. Our unique selling point was that we were a new party and that we would be crazy to get involved with the Liberals.”

Mindful of the toxicity of the Liberal Democrat brand ever since the party entered government with the Conservatives in 2010, the Independent Group has so far resisted any formal partnership with Vince Cable’s party. “The great mistake would be to lose their novelty and link with the Liberal Democrats,” Owen told me.

But he expressed unease at the presence of the former Conservative MP Anna Soubry, who defended the Tories’ austerity programme after joining the group on 20 February. “Soubry is a straight up and down Cameroonite Tory, and that’s got hard edges to it and a lot of very unattractive features.”

Owen, unusually, has moved leftwards with age and speaks of a public appetite for socialism (“1945 socialism is now respectable again in most people’s minds”). “You’ve got to face it, social democracy was hugely damaged by Blair and even, to some extent, by Gordon Brown. We lost the young and Corbyn’s great skill has been to get them back. Social democracy has, for the moment, failed and it’s failing all over Europe too.”

Yet he believes Jeremy Corbyn is incapable of fully harnessing the insurgent mood. “A leader less identified with Trotskyism, Marxism and anti-Semitism than Corbyn would be able to win. Labour won’t lose on their policies… Corbyn’s got to step down, though he can’t be forced out. He’s got to face the reality that he can’t win.”

The legacy of the SDP was to create not one but three new parties (the SDP, the Lib Dems and New Labour). The Independent Group confronts Labour and the Conservatives with similarly existential questions. Both parties, long revered as “broad churches”, must determine the degree to which breadth should be sacrificed for ideological depth. Labour, whose first leader Keir Hardie dismissed “every ism that isn’t Labourism”, could finally be remade as an unashamedly socialist force (a possibility that Tom Watson’s new social democratic group of MPs within the Parliamentary Labour Party – an internal SDP – is designed to counter). The Conservatives, still led by an original Remain supporter, could complete their transformation into Ukip 2.0. Or, faced with the remorseless logic of first-past-the-post and the “big tent” politics it incentivises, ecumenicism could prevail.

I asked Umunna if he would ever consider rejoining Labour under an alternative leader. “No, the two parties were born of a different Britain, products of a different age. They’re past their sell-by dates.”

Much the same has been said by political upstarts for decades. But if the mould cannot be broken now, then when can it?