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London - A wealthy antiques dealer finally admitted on Wednesday that he did murder his seven-year-old daughter.

Robert Peters’ admission came midway through his Old Bailey trial on the morning that his wife was due to testify against him.

His change of plea – he had originally claimed to have had a mental breakdown and was pleading manslaughter by diminished responsibility – came as he was revealed to be a wife beater.

Peters, 56, had previously tried to strangle his second wife Francine, 67, and abused her both ‘physically and mentally’.

Evidence which was not put before the jury showed that during their turbulent marriage between 1994 and 2009, Peters head-butted Francine, slapped her around the mouth and once tried to strangle her.

She only told police about the attack from 20 years ago after Sophia’s murder, recalling: "He grabbed me around the neck, was strangling me. I had marks on my neck."

Friends remembered how the glamorous blogger wore a roll-neck jumper to hide the marks on her neck at the time, although she chose not to report the attack to police, preferring to block it from her memory.

Peters later fantasised about killing his third wife, Krittiya, with whom he had a sexless marriage.

For two-and-a-half years he had an affair with a married Home Office worker he met online, but his Thai wife forgave him and allowed him to come back home after he convinced her of his love. In February last year the philanderer commented on a touching Facebook picture of him looking adoringly at his wife when they met ten years ago in Hong Kong, writing: "It’s the best photo that shows our everlasting love".

Other photographs on social media showed the Jaguar-driving businessman on luxury holidays in Sorrento and New York with his arms around Sophia and Krittiya.

But secretly he was plotting to kill his family and in the months before the murder, Peters trawled the internet for information about ‘serial killers’, searching with terms such as ‘treatment of child killers in prison’ and ‘premeditated murder’.

Just days before he strangled Sophia he searched ‘what is premeditated murder?’ and ‘how long does it take to strangle to death?’

The businessman chose to strike on the last day he would be alone with his daughter before she went back to her £5 000-a-term boarding school after a half-term break.

He waited until his wife had gone out before waking Sophia up in bed by tying a cord around her neck and throttling her for 20 minutes on November 3 last year.

When the terrified girl asked her father what he was doing, Peters said, ‘sorry,’ but carried on.

He then calmly rang police and told them: "There’s been a murder." When officers arrived, he said: "She’s upstairs. I’ve strangled her." His daughter was taken to hospital but she died the next day.

Peters later told officers he had suffered a breakdown. He said he had been hearing voices and thinking of killing his family for weeks so they could be ‘spared the pain and upset when he became bankrupt’. But arresting officers noted that for a man who claimed to have had a mental breakdown, he was oddly calm.

Detectives found no sign that his Kensington-based antiques firm was in financial difficulties and he wasn’t in debt, with a £50 000 Jaguar XK convertible on the drive.

Peters, who ran a business with his twin Richard in an antiques arcade in Kensington, West London, briefly became famous in 2010 after buying a rare Chinese vase, which had an asking price of just £136, for nearly £100 000 after a bidding war. Before the murder he had business assets of £1.3million and bought his home in Wimbledon, south-west London, in February last year for almost £1million in cash.

The court heard that a child protection team had assessed the family a month before the murder and found Peters did not pose any risk to himself or others, despite a history of depression.

When asked why he killed Sophia, Peters told police he was ‘drowning in his business’ and had ‘an OK relationship’ with his daughter but had not loved her ‘in the way that she should be [loved]’.

When asked how he felt after strangling her, Peters said he was ‘without emotion’. He added: ‘Why I killed my daughter is impossible to know, but I did.’

On Wednesday as he was led to the cells after being remanded in custody before sentencing next week, relatives in the public gallery uttered the same question over and over again: "Why?"

Detective Inspector Helen Rance, of Scotland Yard, said: "Sophia was … murdered by the hands of her own father in the most frightening way. She 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."