updated 01/08/2014 AT 9:50 AM ET
•originally published 01/08/2014 AT 10:00 AM ET
Dressed in a baby blue coat, Kate, who will turn 32 on Thursday, checked out the home furnishings and picked up some supplies at one of her favorite department stores, Peter Jones, in London’s Sloane Square.
Also spotted in the store: her mother, Carole Middleton, 58.
Fellow shopper Louisa Smith saw Kate in the cashier section, and noted that there was very little fuss about the VIP.
“You wouldn’t have known it was Kate Middleton,” Smith, an independent distributor for a health and wellness products firm, told PEOPLE. “The shop is always quite calm anyway, and there wasn’t a great deal of people around.”
In fact, said Smith, “It was only when I did a double-take that I realized it was her.”