"House of Fun" is composed in the key of D, written in common time. It is a pop song which moves at an upbeat 126 beats per minute. The song is written in simple verse-chorus form, ending with a repeating chorus fade out (the original 7" release version/mix ends with a sudden keyboard "crash", followed by fairground organ music). The song begins solely with eight drum beats, before the keyboard, bass guitar, electric guitar, trumpet and saxophone are all introduced simultaneously.