Keir Starmer’s speech to the Labour conference in Liverpool was significant for two reasons: for what it said, and for how it went down. As usual, time will tell; but both the speech and the response have the potential to push Labour, and Britain, towards the eventual, but still improbable, reopening of the entire Brexit issue.

Starmer isn’t one of the great natural party conference orators. You still feel that he is learning how to perform some of the baser political skills that don’t always come naturally to a senior barrister. But there was no missing the zinger that he launched into the Liverpool hall towards the end of a well-argued speech about Brexit – or its effect.

All the focus before Labour’s Brexit debate today had been on the second referendum. The speculation centred on how Starmer and the party would navigate the delicate politics of Labour’s conditional embrace this week of a “people’s vote” on the Brexit outcome this autumn.

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When he got to that part of his speech, Starmer was unapologetic. If Labour cannot bring down the Conservative government over Brexit this winter, there have to be other options, he said. These must include a campaign for a public vote.

Starmer avoided getting too deep into the theology of what might be on the ballot paper – the issue that had ranged John McDonnell and Len McCluskey against the party’s pro-European majority in the last 48 hours. But it was the words that followed that set the debate alight.

“Nobody,” said Starmer, “is ruling out remain as an option.” The response in the hall to that was immediate. First an instant volley of applause, but then, from deeper in the hall, and somehow also from somewhere deeper in the gut of the party conference, came the cheering, prolonged and surging, and then the standing ovation.

It was a powerful moment. As someone who has been reporting party conferences for a very long time, I can’t remember all that many like it in any party. It’s rare for a politician, even addressing their supporters, to hit the spot with something truly unexpected and powerful. But Starmer’s embrace of the possibility of remaining in the EU hit that spot unerringly. It was, it seems, an improvised addition to the speech. The words weren’t in the planned text. But the words mattered – and so did the response in the hall. Most were on their feet. The applause went on and on. This was, it suddenly felt, a Labour party that really is up for a fight to preserve Britain’s place in Europe.

That won’t have gone down well with those in the Labour party who see everything in terms of whether it is a challenge to the leader. But Jeremy Corbyn, along with McDonnell and McCluskey, does not want to see Labour drawn down the road of refighting the issue of UK membership of the EU. The reasons for that caution differ: some, like Corbyn, are anti-EU; others, perhaps like McDonnell, are more pragmatic.

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Starmer is tapping into a growing wave of opposition to Brexit, two years on from the 2016 vote. That wave is strong in the Labour party – almost 90% of its members support remain, YouGov found last week. Yet if Labour does indeed campaign for a second vote, and for remaining in the EU in that vote, then it will certainly have to have a strong message for the large minority (35% of its voters) who opted for leave. Claims of betrayal will be loud and potentially lethal. The Tory party machine moved into Get Starmer mode within minutes of his speech ending.

In his closing words, Starmer seemed to be aware of that. The millions who voted for Brexit sent an immense message about the state of Britain, he acknowledged. Much of the rest of the conference Brexit debate was ill-focused and without the quality that Labour remainers will need to summon if this is to go all the way. But Starmer has started something here. He is going to have to carry it through. And, judging by the response in the hall – not always the most reliable guide to public opinion, it has to be said – there are plenty of people willing him on.

• Martin Kettle is a Guardian columnist