Harrods used to have a strict dress code for customers in the past. Now there is no official dress code, but you may be not allowed to enter the store if you are wearing swimwear, athletic singlet, cycling shorts or some other spotswear, flip flops or if you are wearing dirty or unkempt clothing. You have to also avoid wearing clothes with offensive pictures or writings. It is not recommended have a big backpack on your back.
To go to Harrods, there is no particular type of dress required. You have to wear a respectable clothing when visitng the store.