It is fine to order from Harrods, I have ordered Mulberry from them before and had no problems. Their customer services and returns are fine too.
Harrods is one of the UK's biggest and most famous department stores (all the royal family shopped there until Princess Diana went out with the owner's son!).
They are different warehouses, but Harrods is an official supplier of Mulberry bags.
I think (although I am not sure) Harrods may deduct the VAT from the price as you are overseas - whereas Mulberry.com do not. So it may even work out cheaper to buy from Harrods, but I would check with someone else about the VAT just to be sure.