One large swath of voters will not be well-represented in the new parliament. They can be variously described as centrist or centre-left, social democratic, liberal, moderate – choose your own label. It is a large group of people: not just the 3.7 million who voted for the Liberal Democrats, but millions of Labour voters who were more comfortable with Labour in the Tony Blair-Gordon Brown era, and who don’t necessarily describe themselves as “socialist”.

In addition, there are some who normally vote Conservative but applauded the recent interventions of Michael Heseltine and John Major; some who vote Green; and millions of others who don’t have an “ism”. They see politicians as plumbers rather than priests, who “get things done” quietly and competently and without too much unpleasantness. None of these people wanted a parliament packed with nationalists of the English or Scottish variety, or with people advocating what they call “radical socialism”.

I have been active in this centre space for most of the last half century, only to see it increasingly marginalised

I have been politically active in this centre space for most of the last half-century, only to see it increasingly marginalised. Part of the problem relates to our voting system – which, if it were reformed to something like the German, Irish or for that matter Scottish models, would give scope for meaningful representation and cross-party working. But this isn’t going to happen soon: the turkeys aren’t going to vote for Christmas having just been given free range.

The fervent Brexiteers who won this election and the radical socialists who still control the Labour party believe the “liberal establishment” has had it too good for too long, with weaselly compromises; muddy, soulless, consensus politics; the middle way to nowhere. This elite “sold out the country” to foreigners in Brussels, to exploitative multinationals or to some other malign force standing between the government and the people.

In the last parliament, a significant group of Labour and Conservative MPs felt the only escape from the tightening grip of militants in their party was to leave. They had the courage to put their careers on the line, to risk ostracism and put up with abuse. Some stood this time as Lib Dems, others as independents. They were wiped out. All of them. I suspect that those who stayed in the old parties have learned the value of obedience and cowardice.

Play Video 'Devastated': Jo Swinson apologises to Lib Dems for election failure – video

So what is to be done? There is a lot of wishful thinking. Business groups seem convinced that Boris Johnson will now pivot to a soft Brexit, and are already cooing over a few emollient words from the prime minister. But even if he is sincere (breaking the habit of a lifetime), do they seriously believe that his cabinet of Dominic Raab, Priti Patel, Jacob Rees-Mogg and others will conveniently vaporise? Similarly, on the left, there are vague hopes being expressed that if Jeremy Corbyn is replaced by a fresh face (preferably female), it will produce some form of political alchemy, turning unelectable dross into gold. We still hear the plaintive cry that “popular” policies – such as offering lots of things free of charge – are the route to power.

There may also be a resurfacing of the idea that what the country needs is new parties. Usually the dream relies on imagining that Britain is somewhere else, and that we can wish away the first-past-the-post system, which has acted as a roadblock to the Lib Dems and the Greens. This folly should not be repeated. If we are to progress beyond semi-permanent Conservative rule, led by xenophobic populists, we have to change the old parties.

The uncomfortable truth is that Labour, Lib Dems and Greens tend to do well – or poorly – in national elections at the same time, riding or being swept away by the same tides. In this election, numerous potential Lib Dem voters were repelled by what they saw as the risk of Corbyn. This phenomenon boosted the Tory vote, hampering Lib Dem efforts to recapture lost territory in the south-west and the prosperous towns and suburbs Labour struggles to reach.

To adapt to the new reality, my party will have to move on from excessive zealous Europeanism – a cause that led to the unsuccessful revoke policy and has sadly now gone. The Lib Dems must be a voice for “leave” Carshalton – where we lost our excellent, longstanding MP Tom Brake – as much as for “remain” Twickenham. For its part, Labour will have to go back to Gordon Brown’s more disciplined approach to spending – and even to Tony Crosland’s Future of Socialism, written in the 1950s – to remind itself why its clause IV pledge was not a great idea.

Where do the Lib Dems go from here? We can start by working with Labour | Sean Kemp Read more

Labour and the Lib Dems are distinct political traditions with a complementary capacity to beat the Conservatives. This point is misunderstood by those who say each party betrays the other by existing at all. The answer is not a wholesale takeover of one by the other, but more accommodation between the two. If each of the parties will move a little, there is much common ground to find: around constitutional reform, the environment, civil liberties and social justice. As Johnson seeks a trade deal with the EU, there should be a joint defence not just of workers’ rights but of competition policy, where we should continue to look to Europe to restrain the power of companies such as Amazon and Google.

I would hope that the spirit of cross-party groups such as Unite for Remain, More United and Compass can be mobilised around a shared programme beyond Brexit, to give hope to the politically homeless millions in the gaping middle.

• Vince Cable was leader of the Liberal Democrats from 2017 to 2019 and is a former secretary of state for business