Prince William Returns to Kate’s Side But Queen Elizabeth II Won’t Visit

12/04/2012 at 10:00 AM EST

Prince William arrives at King Edward Hospital on Dec. 4

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Prince William returned to the hospital to visit pregnant wife Kate as she spends her second day being treated for severe morning sickness.

William – in a purple sweater, blue collared shirt and black jeans – walked straight into King Edward VII Hospital after exiting a green Land Rover.

Without a wave or signal to the 100-strong waiting media, the father-to-be, 30, had his head down, briefly running his hand through his hair as he strolled through the doors.

Kate, who is believed to be being cared for by Dr. Marcus Setchell (he delivered royal babies for the Countess of Wessex, William’s aunt), was brought to the hospital by William on Monday after her sickness became more acute.

Meanwhile, Palace sources tell PEOPLE that Queen Elizabeth, who was only told Kate was expecting once the couple had decided to head to hospital, will be unlikely to visit.

“She doesn’t normally go because it disrupts the running of the hospital,” the source said. “And the Duchess just wants to recover and get out.”

Kate’s office has cancelled all her planned engagements this week. She was due to appear at a charity day at a London bank Wednesday, a gala for the Centrepoint homeless charity and visit the military tournament this weekend.

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Prince William Returns to Kate’s Side But Queen Elizabeth II Won’t Visit