When, on their first day back in parliament, Labour MPs jeered the phrase “proportional representation”, it was a revelatory moment. There have been times since the election result when we wondered whether the whole multiparty, diversity of British politics was over. But reflecting on the diverse nature of the UK we realised it could not be.

There are, after all, powerful forces that would like the old binary certainties back. It may be one of the few things that the Conservative and Labour parties have in common. Even the BBC would breathe a sigh of relief if it could safely return to its old two-dimensional swingometer.

And just for a moment, it seemed that those awkward little parties – such as the Liberal Democrats and Greens, which so complicate the political struggle – were back to what the whips’ offices used to call them: the “odds and sods”. And that also rules out other, newer players which have a role to play, including the Women’s Equality party and National Health Action party.

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The jeering of PR by Labour’s flanks, suggested that, for all Jeremy Corbyn’s progressive promise, a new politics was still a long way off. Labour’s old hope resurfacing of “one last heave” into singular power, seemed to blind the party to the very new politics it promised. What this made clear, perhaps, is that us odds and sods need to find common purpose in the next few years if our points of view are not to be subsumed into an establishment eager to get back to binary life.

We are activists and members of rival parties – Lib Dems and Greens. We have both been parliamentary candidates for our parties. Our involvement in both goes back three decades or more – and we don’t expect to win plaudits from them for what we are about to suggest. But it seems to us that the combined forces of non-Labour radicalism in UK politics have ambitions for change in Britain that are too alike to avoid some kind of collaboration.

Put aside any notion of mergers – that’s unthinkable and would be counterproductive. Mergers anyway have a bad track record. The recent vote for the Lib Dems was little more than a third of what the Liberal party alone won in 1974.

But equally, it makes sense for both parties to realise that they are fishing in overlapping political waters. Working together to develop informal cooperation and alliances on the ground could bring huge benefits for the kind of diversity, tolerance and sustainable change that both parties are working for.

Of course there are policy differences. Greens might balk at the Lib Dems’ economic liberalism and attitude to trade, while the Greens’ rejection of a conventional economic growth position and promotion of a basic income are distinctive to them. There will always be differences – as there are within all individual parties. But they have concerns, policies and much else in common. And, key to modern, inclusive nations, neither will progress without fundamental democratic electoral reform.

Both parties can also exhibit tendencies that hold them back. Radicalism must be more than just the traditional territory of Jeremy Corbyn’s Labour party. Old-style industrialism and technocratic management has to make way for policies that can press forward with the radical localism, and recognition of planetary environmental boundaries that we need to provide a broader prosperity. Green and Lib Dem collaboration would help remind the other who they are and why they exist.

The two parties already cooperated in a limited way at the recent election. The Lib Dems barely reciprocated the Green’s efforts – only in two constituencies. But this is not a pragmatic argument here about electoral arithmetic – it is an argument about other benefits.

The Greens would get the support and collaboration of a larger body of local activists, parliamentarians in both houses and of elected councillors. They would be able to operate on the ground and influence mainstream business and administration in ways they currently can’t.

The Lib Dems would get an injection of genuine crusading radicalism about something other than the EU, which they badly need. They would also get a more challenging approach to economics. They would get, most importantly, a second chance with the youth vote.

Corbyn’s success has taught us that people respect politicians for what they are for, not what they are against

We believe that they could achieve something – make a difference to the way we live – and could do so immediately, if they were to work more closely together. They could build alliances across the whole radical centre of politics, which could embrace local business and radical manufacturing, from transition towns to the boardroom.

What Corbyn’s success taught us is that people respect politicians according to what they are for, not what they are against – and both of our parties can learn from that. Most of the leaflets that came through our front doors (certainly the Lib Dem ones) were long lists of issues they were going to “fight” and “resist”. Which is fine, up to a point, as long as you realise how far it falls short. We can’t go on like this. Nor can we let the old-fashioned right and left go back to carving the world up between them. We need to put forward a radical, different vision – one that is properly pragmatic in the sense that it matches in ambition and scale the immediacy of environmental and social challenges.

So it would be a framework that allows all smaller progressive parties to work together and to put up candidates who can get the wholehearted support of all. Not mergers, but forms of co-operation that result in policy debate and creativity rather than a set of lowest common denominators.

If it works, and all such parties experience a genuine parallel growth, it could build the foundations of a new political movement for change. The energy of such a movement would come from below, and any emerging figureheads could be drawn from a much wider gene pool than Westminster’s binary opposition parties.

• David Boyle and Andrew Simms are both co-directors of the New Weather thinktank