The new parents were pictured leaving the Palladium theatre after watching I Can't Sing!, the X Factor-inspired musical which sees EastEnders actor Nigel Harman star as Simon.
The 54-year-old music mogul seemed full of praise for Harry Hill's musical comedy, tweeting "It's difficult to describe because I have never seen anything like it before. I hope you love it as much as I do.
"And seriously expect the unexpected!" He added.
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After taking the time to greet fans who had gathered outside the theatre, Simon headed for dinner with Lauren at the Scalini restaurant in Chelsea.
For her night out in the British capital, Lauren chose a chic black dress with lace detail and black and gold heels, while Simon sported a white shirt and blue jeans.
The couple chose to leave their son Eric at home during the evening, possibly in the care of Simon's mother Julie who was eager to meet her baby grandson when he arrived in England.
Earlier in the week Lauren was seen out-an-about in London with three-week-old Eric. The socialite, who also has an eight-year-old son named Adam from her marriage to Andrew Silverman, carefully cradled her newborn as she stepped out in the city with Simon.
Eric Philip Cowell, who is named after Simon's late father, was born in New York on Valentine's Day.
Two days after the youngster's arrival Simon released a series of photos of Eric with his proud parents.