This is good design. The bags are serviceable — you get your stuff home without worrying whether the bottom of the bag will collapse and open. The colour, Pantone 109 yellow, stands out on the crowd. You can see someone who been shopping at Selfridges from a block away on a crowded London street. (Either they have been shopping there or they are craftily wanting you to think they have been shopping there and making use of the iconic bag while they do their retailing at lesser stores.) But most of all, they bag is designed to do what a shopping bag should do: announce loudly the name of the store to everyone within eyeshot. The colour does most of the attracting, and the restrained typeface (derived from Franklin Gothic) in contrasting black says that this store is classy and hip.
I cannot say that I go shopping in Selfridges just to get a shopping bag, but if I am equidistant between Selfridges and an equivalent store, I’ll head to where I get a yellow bag.