In under a week and a half the new Independent Group of MPs has changed the course of British politics. On whatever side of the fence you sit, that is a stunning achievement.

Almost one in five voters are now said to be considering voting for a nominal Independent Group party. The creaking door of Labour’s move towards a second referendum has been given a shove – its familiar caveats notwithstanding. And they have coaxed more Tory MPs to their midst in a matter of days than the SDP-Liberal alliance managed in several years of trying. Heidi Allen, Anna Soubry and Sarah Wollaston are exactly the type of Conservatives one would handpick for any new alignment. In short, this is a big deal.

To be sure, there is undoubtedly something of the Alexandria Ocasio-Cortez effect here. It is certainly easier to appeal to more people when you are fresh faced, and haven’t yet had to make any compromises. Creative use of social media, Nando’s nights out or otherwise, helps too.

But there is also a serious hole at the centre of our politics. When the “don’t know” candidate for prime minister is at 42 per cent (3 per cent ahead of Theresa May and a whopping 26 per cent above Jeremy Corbyn), there are clearly millions of voters who don’t hold much of a candle for either of the two major parties.

The harshness and vitriolic certainty of the left, combined with the swaggering incompetence of the right, has left many with nowhere to go. New thinking is needed.

Which MPs defected to form Change UK? Show all 12 1 /12 Which MPs defected to form Change UK? Which MPs defected to form Change UK? Change UK Details on the individual MPs are in the following photos Reuters Which MPs defected to form Change UK? Heidi Allen Anti-Brexit MP for South Cambridgeshire resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Chuka Umunna MP for Streatham since 2010 and prominent People's Vote supporter PA Which MPs defected to form Change UK? Anna Soubry The prominent anti-Brexit MP for Broxtowe resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Luciana Berger MP for Liverpool Wavertree since 2010, resigned from the Labour Party over bullying and anti-semitism PA Which MPs defected to form Change UK? Sarah Wollaston Anti-Brexit MP for Totnes resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Joan Ryan MP for Enfield North resigned from the Labour party on February 19 citing its tolerance of a "culture of anti-Jewish racism" PA Which MPs defected to form Change UK? Ann Coffey MP for Stockport since 1992 Chris McAndrew / UK Parliament Which MPs defected to form Change UK? Gavin Shuker MP for Luton South since 2010 Getty Which MPs defected to form Change UK? Chris Leslie MP for Nottingham East since 2010 PA Which MPs defected to form Change UK? Mike Gapes MP for Ilford South since 1992 PA Which MPs defected to form Change UK? Angela Smith MP for Penistone and Stocksbridge since 2010

Back in the 1980s and 1990s Bill Clinton and Tony Blair reinvented what it meant to be a progressive in changing economic circumstances. They did so within the existing major parties of the centre-left and thus, for some, form a powerful argument for sticking with Labour. There are many reasonably minded Labour MPs who are battling hard to reform their party – and who deserve commendation for their courage. As my forthcoming book March of the Moderates shows, there would have been no New Labour without Neil Kinnock.

For sure, it cannot be easy to continue to caucus with left-wing MP Chris Williamson, particularly if the latest Parliamentary Labour Party meeting is anything to go by. It is to be hoped that the responsible elements within Labour continue an open dialogue with the new splinter group, and, one hopes, there have been some new WhatsApp groups created of late.

But there is another lesson from the 1980s. Back then the SDP formed an important space for rethinking what progressive politics should be. It engaged with the realities of Thatcherism, rather than the priorities of left-wing special interests. In doing so, it managed to constrain Thatcher’s majority in 1983, rather than augment it.

Such a move is again needed. Too many mainstream progressives have stopped thinking – evidenced by the decline of former heavyweight organisations such as the Institute for Public Policy Research and the occasionally Pravda-esque New Statesman. Post-Brexit Tim Montgomerie arguably forms something of a depressing counterpart on the right. The need for instant hot takes required by Twitter probably doesn’t help here.

That said, free of Corbyn ally Richard Burgon and columnist Owen Jones, the Independent Group is now free to appeal to working- and middle-class voters whose minds aren’t closed. Without the anchor of the European Research Group, One Nation Tories can better redirect their energies.

As YouGov’s Matthew Smith points out, the British public is more pragmatic than its hitherto rigid political parties would suggest – and it prioritises outcomes over and above ideological prescription. Professor Glen O’Hara has mapped out some interesting areas where this could go, particularly on deprioritising the cutting of university tuition fees – in effect a middle class tax bung.

Alongside this, the Independent Group could even opt for a more dramatic, counterintuitive measure. Tony Blair, for one, has backed the use of “land value” taxes. A party with a progressive offer on the redistribution of wealth, whilst taking a more restrained view on income, might have much going for it – and form a coherent third way between left and right. I’ve argued previously for the merits of a financial transaction tax for much the same reasons. There is potential here – particularly for a new force which is more credible than Corbyn in other areas, such as defence and law and order. A pragmatic Blairism for the 2020s may end up in different policy positions from its 1990s predecessor.

The Independent Group does not, of course, control the flow of events. Theresa May has cards to play, as does Jeremy Corbyn. But if it can peel away another 10 or 20 MPs, lock down a list of five or six signature pledges and, crucially, elect a leader, it is in business.

If an election is called imminently, it will need a pact with the Lib Dems, but over the long term it will need its own identity. Luciana Berger, Mike Gapes, Chuka Umunna and others have shown that there is still an innately reasonable element within British politics – and good for them.