Taking the UK out of a European human rights treaty to quell rightwing anger over immigration would be a mistake, the new head of Britain’s equalities watchdog has said, as she warned against the demonisation of people who migrate to the UK.

Mary-Ann Stephenson, who became chair of the Equality and Human Rights Commission in December, said the European convention on human rights (ECHR) was part of a framework that provides rights most people would agree were fundamental. But she said the tone of public conversation on it was often dangerous.

“I think it’s really important that we have honesty in the way that we talk about human rights, and that we also have a recognition that the demonisation of migrants – creating this idea that migration causes huge risks for the country – can make the lives not just of migrants to the UK, but of ethnic minority UK citizens, very, very difficult.”

Stephenson noted a “real risk of people using, quite often, cases where human rights arguments were made in court but were not successful” when discussing the ECHR.

She pointed to research from the University of Oxford earlier this year that highlighted “several high-profile examples of misleading coverage, including the so-called ‘chicken nuggets’ case – widely reported as the prevention of an individual’s deportation on the basis of his child’s dislike of foreign food, despite the decision not being based on this detail and having already been overturned”.

Political debate has ramped up around the UK’s membership of the ECHR – often in relation to cases in which the government seeks to deport people. Some on the right have claimed the convention hampers those efforts. Both the Conservatives and Reform UK have said they would quit the international treaty.

The Labour government is reviewing human rights law to make it easier to win deportation cases. Changes to article 3 – prohibition on torture or inhuman or degrading treatment – and article 8 – the right to family life – are included in the government’s plans to overhaul the asylum system, which have both been relied on in high-profile cases.

Stephenson described the convention as “really important” because it was incorporated into the UK’s Human Rights Act and said leaving would weaken the rights everyone depends on.

She gave as examples the supreme court judgment in relation to the investigation into the rapist John Worboys, which ruled police could be held liable for serious failures – and another involving the threatened separation of an elderly couple when one needed to go into residential care.

“These are all sorts of cases where most people would think: ‘That’s the sort of thing we would want to see. Those are the sorts of rights we would want to have.’ And so I think leaving the European convention is a mistake. It weakens the rights that all of us depend on.”

Earlier this month, the chief of the body that oversees the convention said member states had taken an “important first step forward together” in agreeing to look at changes to tackle migration within its legal framework.

The Conservative home affairs spokesman Chris Philp described Stephenson’s remarks as a “disgrace” and claimed “the left” was trying to paint “those opposed to mass immigration and illegal immigration as racist”.

“This nonsense has to end. It is completely wrong that Labour’s new human rights chief dismisses legitimate concerns about mass migration and crimes committed by foreign nationals - including the recent spate of rapes and sex attacks committed by small boat illegal immigrants,” he said.