Famously, in the 1970s BBC comedy "The Fall and Rise of Reginald Perrin," Reggie opened a doomed (he hoped) shop that sold old bits of trash and scrap recycled into completely useless items. He called it "The Grot Shop." (To Reg's horror, the shop was wildly successful, leading to a string of Grot Shops and, eventually, Grot Industries.)
Something that is "grotty" has a look of filth about it.
"It looks like a grotty old shoe, to me."