Essex police have defended their decision to investigate the Telegraph columnist Allison Pearson over a social media post, saying she is accused of “inciting racial hatred” not of committing a “non-crime hate incident”, as she had claimed.

The row over Pearson’s tweet has been splashed across the front pages of the Times, Telegraph and Mail this week. Leading figures on the right, including the new leader of the Conservative party, Kemi Badenoch, and the former prime minister Boris Johnson, have leapt to her defence.

In his Mail column on Saturday, Johnson said the incident was “redolent of the Soviet Union at its worst” and called on the force to drop its investigation. Meanwhile, Badenoch called for hate crime laws to be reviewed in light of the incident in comments splashed on the Telegraph’s front page on Saturday.

Non-crime hate incidents are offences motivated by hostility or prejudice towards people with a particular characteristic that do not meet the threshold of a criminal offence.

Essex police said Pearson had been told she was being investigated for inciting racial hatred, which is a criminal offence.

In a statement the force said: “Officers attended an address in Essex and invited a woman to come to a voluntary interview. They said it related to an investigation into an alleged offence of inciting racial hatred, linked to a post on social media.

“We police without fear or favour and that’s why we respond to alleged offences which are reported to us by members of the public.

“For clarity: a complaint of a possible criminal offence was made to the police and this is why we called; to arrange an interview. Everyone was polite and professional throughout the brief conversation.”

The force says it has complained to the Independent Press Standards Organisation (Ipso) “on a matter of factual accuracy”.

According to the force, the officer said to Pearson: “It’s gone down as an incident or offence of potentially inciting racial hatred online. That would be the offence.

“Because of what’s been alleged and the evidence that we’ve got, I need to just ask you some questions.

“It’s what’s been alleged and if there’s an offence we need to ask questions about then we need to do that.”

The force said it “supports free speech” and “does not support inaccuracy” and added: “If an alleged crime is reported, it is investigated. There is no public interest in falsehood.”

Pearson said she had been “dumbfounded” by the visit by the police.

She added: “Whatever I did or didn’t tweet, if somebody found it offensive, that to me is still not a reason for two policemen to come to my house on a Sunday morning.

“You know, they don’t do that for burglars, do they? We know policing is under-resourced and they are unable to attend often quite serious crimes.”

Several prominent Conservatives came out in support of Pearson, including the shadow home secretary, Chris Philp, who said: “Only where the criminal threshold is met should police become involved. I do not think officers should be policing thought – only actual crimes.”

Former prime minister Liz Truss said the investigation was “bullying” and an “affront to free speech” while Elon Musk quoted an X post about the incident and said: “This needs to stop.”

The Guardian revealed the post at the heart of the storm was an alleged retweet by Pearson of a photograph posted several months ago, amid heightened tensions over the policing of pro-Palestine protests. It shows a group of people of colour posing with a flag unrelated to the conflict, flanked by three police officers.

Pearson allegedly wrote a tweet condemning the Metropolitan police: “How dare they. Invited to pose for a photo with lovely peaceful British Friends of Israel on Saturday police refused. Look at this lot smiling with the Jew haters.”

The people in the picture were holding a flag used by supporters of the Pakistani political party Pakistan Tehreek-e-Insaf (PTI). The flag has the word “Pakistan” written on it. The picture was taken in Manchester, not London, and the officers were from Greater Manchester police, not the London force.

On Friday the Telegraph said Pearson had “deleted the post after the mistake was pointed out”.

The original complainant told the Guardian that Pearson’s post was “racist and inflammatory” – which she denies.