The pair dined at a Notting Hill eatery with members of their household staff on Tuesday

By Simon Perry
December 18, 2012 02:00 PM

Prince William and expectant Kate have started their royal Christmas celebrations.

The Duke and Duchess enjoyed a private lunch with their household staff in London on Tuesday, a St. James’s Palace spokesman confirms to PEOPLE.

The festivities took place at Bumpkin in the Notting Hill neighborhood, and the group dined in restaurant’s “Queen’s Room,” which features a large portrait of Queen Elizabeth.

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Earlier this week, Kate stepped out for her first official engagement since being hospitalized for severe morning sickness.

The question remains about where the royal couple will spend the Christmas holiday.

They may keep with tradition and go to Sandringham House in Norfolk, where they celebrated last year, to be with the Queen and the rest of the royal family. Or they may spend the holiday in Bucklebury, Berkshire, with the Middleton family.