If the test of a speech is how effectively it generates headlines and dominates conversations, Tony Blair’s call for a Brexit rethink today was a resounding success. Less so, perhaps, if the test was to persuade people who do not agree with him already.

Mr Blair always commands attention as the only living British politician to have won three elections and served a decade as prime minister. That experience furnishes insight deserving of an audience. But such insight is routinely obscured by debate about the integrity of the man. Anyone who served so long will animate partisan feelings; Mr Blair’s unusual fate is to have aroused some of the most passionate hatred within his own party.

It is possible to believe that some of the opprobrium is earned, yet also to think that the argument advanced by Mr Blair on Brexit is sound. His case is that Britain voted to leave the European Union without an account of what that would involve in practice. As the terms of separation become clear – if it appears that the government is wedded to a ruinous version of Brexit – it is reasonable to argue for a different course.

This is not a call to overturn the verdict of the people in last year’s referendum. It is a call to those who doubted the wisdom of that verdict to raise their political game, to find new arguments and new strategies fit for the post-referendum context. Context is everything. The path of severe rupture from the EU chosen by Theresa May was not the only possible interpretation of the referendum mandate. It is a road down which the prime minister has been steered by the most radical fringe of her party, bulldozing moderate opinion in Conservative ranks.

The Labour party’s acquiescence to Mrs May’s timetable articulates chaos and weakness in Jeremy Corbyn’s office more than coherent opposition strategy. In other words, the Brexit trajectory that Britain now faces is an accident of weak leadership on both sides. Other trajectories are available. To assert that fact is not undemocratic. The deeper offence against democracy comes from those Europhobic ultras who try to stifle every murmur of dissent with demagogic nationalism – as if reasonable Brexit-scepticism is no better than treason.

In a less febrile atmosphere, Mr Blair’s argument would hardly be controversial. The disproportionate impact of a single speech testifies to a lack of authoritative opposition and a level of infantilisation in the way the debate has been conducted on both sides. Leave supporters are too casually depicted as racists or Little Englander nostalgics. Pro-Europeans are dismissed as embittered “remoaners” and arrogant elitists, detached from the concerns of “ordinary” people. Since the referendum result was so close, with millions in each camp, it is inconceivable that either caricature can be justified.

It is unfortunate that Mr Blair embodies the stereotype on his side of the debate. Few people conform so neatly to the image of a globe-trotting metropolitan. That makes him a problematic messenger for a putative pro-European insurgency, even before all the other baggage of his decade in power is weighed. Yet, when Mr Blair speaks, audiences listen – and on this occasion he had something of substance to say. His was a well-reasoned case made with judicious authority – and by framing the argument between supporters of Brexit “at all costs” and the rest, he showed a familiar skill for appealing to all those, leavers as well as remainers in this case, who abhor the obsessive or fanatical approach. That in itself is worth appreciating in a week when the US president degraded his office and alarmed audiences in a rambling press conference marked by petulant incoherence and wilful ignorance. Mr Blair reminds us what it was like to have grown-ups in charge. Whether he can still be effective in advancing a cause is different. He is entitled to try. No one else is making the pro-European case with much impact.

British politics is in a state of turbulence. Next week sees unpredictable byelections in Labour-held seats in Staffordshire and Cumbria that might just as easily offer reprieve or humiliation for Mr Corbyn; embarrassment or breakthrough for Ukip; triumph or disappointment for the Tories; more evidence of a Liberal Democrat revival or none. The trends have rarely been less clear. This can be alarming to those who like stability, but reassuring to those who feel beaten and demoralised by recent events. That is the most vital part of Mr Blair’s message. New arguments to protect Britain’s place in Europe and the world can still be made and won – even by Mr Blair.