The Duke and Duchess of Cambridge
04/30/2011 at 11:00 AM EDT
woke up as the Duke and Duchess of Cambridge Saturday morning – and headed off for a little privacy.
After spending the first night of their married life at Buckingham Palace following an evening of partying
, the newlyweds were seen strolling the Palace grounds hand in hand, thanking staff before they were whisked away by helicopter.
And while she may be royalty now, the Duchess made a very down-to-earth footwear decision: She wore the same wedges Saturday morning as she did for her wedding rehearsal just a few days before.
Only 24 hours earlier, the couple had been been making separate departures, en route to Westminster Abbey for their wedding
But what of their top-secret honyemoon?
"The Duke and Duchess of Cambridge have chosen not to depart for a honeymoon immediately," the Palace said in a press release.
"Instead, after spending the weekend privately in the United Kingdom, The Duke will return to work as a Search and Rescue pilot next week. The locations of both their private weekend and their future honeymoon, which will be overseas, will not be disclosed in advance."
As for the father of the groom, Prince Charles, he was seen Saturday morning taking the Aston Martin
– one of the big stars of yesterday's show – for a morning drive.
A source tells PEOPLE, "Charles pulled out of Clarence House around 10 a.m. in his Aston Martin and zipped over to Buckingham palace to see the couple off. He looked very pleased."
With reporting from CHARLOTTE TRIGGS in London