Darren February took valuables from a safe at the Holland Park property as Mr Cowell and his family slept.
Cowell said in a statement to the court: "The whole incident has been very traumatic and there is a constant fear that it may be repeated and that it may be worse next time."
"This incident has caused me great concerns about the security of my family. On reflection I am very scared of what could have happened to my son if the burglar had gone into his room.
"I could not bear to think of the consequences and also a lot would have happened if the burglar had come into our room."
February, who faces a lengthy jail sentence today, is already behind bars, serving eight and a half years for causing the death of biker Kenneth Baldwin.
The thief has a criminal record stretching back to when he was just 12-years-old, including 37 burglaries on wealthy west London households and a four-year prison sentence in 2013 for assault, affray, criminal damage and theft.
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