From someone who lives in England....
I agree, go check out Harrod's. BUT, don't do what I did and walk in with a backpack.
I just went to go look at their cool decor and didn't plan on buying anything. The second I walked in, a security guard said "Excuse me, miss, please carry your rucksack in your hand." Like it's such a nice store that my backpack would ruin the scenery.
Anyway.....
Harrod's is expensive though.
"Next" is a good store; it's where I shop. Though, I think they have those in the US. Also, Top Shop is pretty hip. Sometimes nice things can be found in Debenham's department store. If nothing else, go into department stores to check out the ladie's hat department! They are so fun to try on - like you're going to a royal wedding or something.
I've never shoped at Marks and Sparks for clothes, only groceries - can't help there.
Oh, and by the way, the name of the place Lisa Fishman recommended is "Covent Garden".
Have fun and PM me if you have any other questions!
......Kelly