The sight of David Lammy and Richard Hermer arriving together in Strasbourg to demand new constraints on human rights law would have been unthinkable even a year ago. But as one ally says, quoting The Leopard, “If we want things to stay as they are, things will have to change.”

It was that sentiment that convinced Lammy’s predecessor, Shabana Mahmood, now home secretary, that the UK should join the push to seek a declaration to reform how the European convention of human rights should be interpreted.

It was Mahmood who has made the determined argument from inside government that Labour must act to prevent the perceived overreach of human rights law or risk far worse if they lose the next election to the hard right.

And it is that message – reform or die – that has won over a considerable number of Labour MPs, including Lammy, a veteran of the struggle for racial justice and Hermer, one of the most eminent human rights barristers of his generation, who were once considered sceptics of that mission.

For many, it will be jarring to see how the UK has come to argue alongside countries like Hungary and Italy that the ECHR must advise domestic judges they should narrow the definition of “inhuman and degrading treatment” as well as put curbs on the right to family life.

But Lammy and Hermer are in Strasbourg alongside others on the centre-left in Europe too – Norway, Denmark, Iceland, Ireland – because of their view that the only way now to salvage the ECHR is to reform how it can be applied.

Ministers believe the UK can be a particularly influential voice in the debate. Under Keir Starmer, another former human rights lawyer, there is no question of the UK leaving the convention itself. That matter is not up for discussion.

But the UK wants to be able to demonstrate quickly that national interest can be served and the public protected while remaining a member of the ECHR.

Since this autumn, the argument has become even more acute, with the Conservatives also now committed to leaving the ECHR, alongside Reform UK who have long made that argument.

Starmer himself – who wrote his first article for the Guardian back in 2009 in defence of human rights law – is convinced that there are genuine instances of the convention being interpreted too widely, especially by the lower tribunal.

Too often, those are caricatures in the right-wing press, myths about how foreign judges won’t let criminals be deported because their children prefer the taste of British chicken nuggets.

But there have been more serious cases in recent years that have worried ministers, of child rapists permitted to stay in the UK because of the overcrowded nature of Brazilian prisons or some instances where healthcare systems not deemed as advanced in other countries have prevented the deportation of criminals.

This, ministers say, is their target for narrowing the interpretation of the law, not preventing genuine survivors of torture from claiming asylum.

In almost every case – despite what Nigel Farage or Robert Jenrick say – it is not actually judgments from Strasbourg causing the issue, but the way that domestic immigration tribunals have been interpreting the convention.

What the UK and its 27 allies in this push are is seeking is a spring declaration from the ECHR which sets out stricter ways that domestic courts should interpret both family life and degrading treatment.

Taken together, ministers hope those changes will see far fewer cases of dangerous individuals having their deportations prevented by the courts – and thus less ammo for the far right to use.

The counter argument which many charities and campaigners have made is that the answer to the far-right challenge to human rights law is not to try to appease them, but to defend the principle even more robustly.

Unless Starmer is also prepared to be more vocal on that principle, there is a real risk that actions he hopes will ultimately help preserve human rights will alienate even more of his progressive voters and do little to convince any anti-immigration voters on the right that he has gone far enough.