She later posted a tribute on Facebook saying: "I love you a lot and love you forever sweetheart."
Sophia is just started studying at a boarding school, the Evening Standard reported. Her friends and family are said to be heartbroken.
Three-times-married Peters didn't appear in court for a brief administrative hearing today.
Neighbours said Peters had only to moved the area recently and the property was bought in February for almost £1 million ($1.89m).
A neighbour, who didn't give his name, told MailOnline: "It's tragic. I have spoken to him four or five times and he struck me as a reasonable and decent sort of chap."
Another said: "From the little we found out about him over the time he has been here, he has an antiques business with his brother somewhere.
"I have spoken to him two or three times. He seems a perfectly reasonable guy, a normal guy, but we could not make out what his family arrangements were.
"His car used to disappear, others used to be there, other cars would come and go."
Peters is said to have business assets of around £1.3m. He runs an antiques business with his twin brother Richard in London.
His third sibling, Paul, is also involved in an antiques business in North Yorkshire.