From 1926 to 1972 the London Zoo held regular chimpanzees' tea parties during the summer months. These parties did indeed involve chimps sitting at an outdoor table on regular chairs and drinking tea from regular teacups. These were a fairly popular tourist attraction, and became very well known in the UK. From the 1950s to 2002, this meme was bolstered by a series of PG Tips tea TV commercials, which featured their own set of chimps having tea; these chimps were a bit fancier, in that they were dressed up in human clothing, an indignity that the zoo never attempted.
The phrase "chimpanzees' tea party" has entered into fairly common usage in Britain to refer to a chaotic, ridiculous, or messy situation. This reference is completely lost on Americans.