I don't have a lot of London recommendations, however, you did mention you and your friend will be doing some shopping so I have one dining recommendation.

Harvey Nichols (called Harvey Nicks by the locals) is a wonderful high end womens store right next to Harrods. Upstairs (5th floor) they have their gourmet department as well as a few dining choices. You would have about 4 choices up there, 2 are typical lunch fare - sandwiches, soups, wonderful grilled salmon - and one is a sushi counter where small plates of food come round the counter via a "train". Select the ones you want, the color of the plate determines the price and eat what you want. There is also an espresso bar that has pastry and small sandwiches as well.

Though I've been to London a couple of times, I don't know it well. I'll be there again in Sept, so if you find some nice dinner places that won't break the bank, let me know. And if you find a website to the markets, I'd love to know about that too. Thanks.

Enjoy your travels.

Candice NYC