One reason for having a lower circuit height is the lateral size of the circuit is smaller. An example is RAF Newton close to Nottingham (Tollerton) airfield. Both the circuit heights were 800 ft (above respective aerodrome levels) because they were within about 3 miles of each other.
Yes, I know RAF Newton is now (very sadly) closed but the circuit height at Tollerton has remained at 800 ft.
Another reason is combined fixed wing/helicopter traffic. I don't know whether it's the same now but Oxford used to have a fixed wing circuit height of 1,200 feet with the helicopters having of 700 ft with opposite circuit directions - this meant you had 500 ft separation from helicopter traffic when overflying their live side at 1200 ft in a fixed wing a/c.
1,000 ft is the norm - any differences should be publishes in the AIP.