The easiest game to play as a political pundit is to say: this set of election results proves I was right and vindicates the strategy I have recommended. But anyone claiming that these results offer clear answers for Labour are simply expressing what they would like the party to do. Some voices are arguing that Labour is being punished for not backing a second referendum; others that it is being damaged for whipping its MPs to vote for it twice; and many contend that Labour is being damaged because it is triangulating over the dominant political issue of our time. They are all correct. That does not, however, offer a guide as to what the party should do next.

The Lib Dem surge is real. But Brexit isn’t the only story of the local elections | Lewis Baston Read more

One thing is clear: for the Tories, these are catastrophic results. Ignore the party’s cynical attempt to massage expectations, this is comparable to the shellacking Gordon Brown’s disintegrating government received during its death throes. As for the Lib Dems, that their revival is being presented as sensational is more indicative of just how far into the abyss the party fell. These seats were last contested in 2015, when the party was virtually wiped out as a national political force; they are reviving in what were their traditional heartland seats. Yet simply conflating all of the Lib Dems’ surge from oblivion with remain’s revenge is simplistic. As John Curtice – Britain’s most distinguished psephologist – puts it: “So it seems easier to interpret this as evidence of Liberal Democrats recovering from the coalition, being the party of protest, and that’s the basis of their success, rather than necessarily a rush of enthusiasm for the idea of a second referendum.”

Labour has made progress in many areas it needs to win to form a government: winning Trafford, gaining in Plymouth, Worthing, Telford and Wrekin, and Peterborough; and while it didn’t win Swindon, its vote jumped by eight points, equalling the Tories’s share and giving the party hope of gaining the key bellwether seat of the town’s southern constituency. In the Midlands and the south, there has been a significant Tory swing to Labour. But let’s not delude ourselves that these are good results for Labour – they’re not.

In different areas – and, often, in the same place – both remainers and leavers have given Labour a kicking. Some natural Labour voters, furious over a neverending Brexit debacle, have defected to the Greens, themselves benefiting from the welcome boost to environmental issues thanks to Extinction Rebellion; while in Ashfield, Bolsover and Bolton, Labour have been clobbered by independents, many of them ardent Brexiteers. In Sunderland, senior Labour voices complain that talk of a second referendum has alienated voters; in Brighton, voters angrily denounce the party for not embracing a people’s vote.

Some will try to frame this all as the remainers’ revenge. But the Brexit party did not stand and many angry leave voters abstained; watch the narrative shift if – as currently seems likely – Nigel Farage’s party triumphs in the European elections. While much of the media will focus on Labour’s losses rather than the Tories’ disastrous results, Jeremy Corbyn’s party is likely to end the day with a significant national lead. At face value, it seems Labour is heading for a minority government that would dilute and obstruct its transformative ambitions. But there are big caveats here: extrapolating from low-turnout local elections – in which the most motivated voters have the greatest political impact and younger supporters who powered the Corbyn surge are more likely to sit it out – is profoundly problematic. Remember in 2017, when Labour was battered in local elections, then four weeks later won 40% of the vote and deprived the Tories of their majority?

Corbyn’s Labour is founded on a sense of political insurgency, on vibrant anti-establishment politics: that’s how it defied the laws of politics in 2017. Who’s to say that could not happen again? As long as Brexit dominates, its popular domestic programme of taxing the rich to end austerity, scrapping tuition fees or bringing utilities into public ownership languishes on the fringes of political debate. The party is left resembling the other discredited contenders, sitting on the fence, mealy-mouthed, triangulating.

One of the great successes of both the continuity remain and leave campaigns has been to make those seeking a compromise on Brexit seem morally reprehensible, the useful idiots for whichever side you don’t like. That middle ground has been deliberately and successfully squeezed, at least in the national political debate. And so Labour are told to embrace the evangelical remain cause. But that ignores the political reality: even if Labour backed a second referendum, there aren’t the votes for it in parliament, and campaigning for such an outcome would write off many of the leave seats the party will need if it is to win an election.

There will be many siren voices arguing that there are simple answers for Labour. As long as Brexit dominates, there aren’t. The party’s left-populist message is sidelined, and it risks alienating the remain and leave voters it needs to win an election. Sometimes the honest answer is there are no easy solutions, and anyone arguing otherwise is kidding themselves.

• Owen Jones is a Guardian columnist