An antiques dealer who strangled his seven-year-old daughter in an act of “pure selfishness” has admitted murder midway through his trial.

Robert Peters, 56, throttled Sophia with a dressing gown cord while alone with her at his family home in Wimbledon, south-west London, in November. He called 999 to report what he had done and the child was taken to hospital, but died the following day.

The killing came just over a month after Peters, who had depression, was found not to be a risk to himself or others by a child protection team.

Peters had admitted manslaughter but denied murder, claiming he was hearing voices at the time. But three days into his Old Bailey trial, he changed his plea, watched by Sophia’s mother Krittiya – his third wife – and family members.

Peters had recently ended a two and a half year affair with a married Home Office official he met online.

His wife had caught him on the phone with the woman but forgave him and he moved back home, the court heard. Peters was also worrying about his finances and claimed his Oriental antiques business in Kensington was going bankrupt, even though he owned a Jaguar car and had plenty of money in the bank.

In the months before the killing, Peters searched the internet for “serial killers”, “treatment of child killers in prison” and “premeditated murder”.

He chose his opportunity to kill his daughter before she was due to return to her £5,000-a-term boarding school after the half-term break, waiting until his wife went out.

When officers arrived at his Blenheim Road home, Peters calmly told them: “She’s upstairs. I’ve strangled her.”

When Sophia was found she had a weak pulse and was taken to hospital, joined soon after by her mother, who was escorted there by police.

Sophia was treated in intensive care but died from brain damage the next day, on 4 November 2017.

After his arrest, Peters said he had not been a good father and was experiencing a breakdown. He said he had been thinking of killing his wife and family for several weeks so they could be “spared the pain and upset when he became bankrupt”.

Peters told police he had been visited by a child protection team and feared Sophia would be taken into care.

However, an assessment had concluded on months earlier that he was not a risk to himself or others and the case was closed.

It can now be reported that Peters’ second wife, Francine, claimed he had throttled her during their marriage, which ended acrimoniously in 2009. She said in a statement after the killing: “He grabbed me around the neck, was strangling me. It was on a hot summer month. I had marks on my neck.”

She also alleged he was controlling and had headbutted her and slapped her face.

But Jim Sturman QC, defending, dismissed her account, which was not put before the jury, saying it “never happened”.

he home of Robert Peters in Wimbledon, south-west London. Photograph: Ryan Hooper/PA

Mr Justice Edis remanded Peters into custody to be sentenced on Monday.

DI Helen Rance of Scotland Yard said: “Sophia was an innocent seven-year-old girl, much loved by her mother, brother and friends. She was tragically murdered by the hands of her own father in the most frightening way.

“Sophia had her whole life ahead of her, which was taken away so cruelly in an act of pure selfishness. Robert Peters has shown no remorse for the murder, and initially maintained a defence of diminished responsibility. However, due to the strong evidence against him, he has changed his plea to guilty.

“This was a particularly traumatic case to deal with for all concerned, and I hope that this conviction brings a degree of closure to Sophia’s family.”