Fritz and I had a day out in Belgravia/Knightsbridge.
We started at Mungo & Maud, one of our favourite pet shops. Then we walked to Sloan Square and up Sloan Street. Everywhere was dog-friendly - Christian Louboutin, Smythson, Mont Blanc, Moncler, Louis Vuitton and Missoni. At Smythson they even told me to let him off the leash and let him run around the shop. I kept him on-leash at Louboutin, though, since he loves to eat shoes.
And then we went to Harrods, which I certainly recommend for pet-lovers. Harrods Pet Kingdom sells animals so for health reasons you must bring proof of vaccinations/a pet passport with you. Dogs are not allowed into the rest of the store so if you report to Door 3, the security guard will ring up to the Pet Kingdom who will send someone down to escort you. They have a great selection of animal toys, treats and accessories - and even a pet bakery! And Fritz made friends with the helpful staff as you can see below.
And if you want to shop in the rest of Harrods? Leave your dog at the dog spa! They offer everything from grooming to massages. There is also a daycare service where you can leave your dog whilst you wander around (booking recommended).