The early Spitfire actually could fly upside down.
What it couldn't do was "bunt", that is, nose over into a dive, without a short period when the engine "cut" due to fuel starvation, this problem being cured by alterations to the carb system.
To follow a diving enemy, the Spitfire did a half roll and then the pilot "pulled" to initiate a dive, before rolling level again. Seemed to work quite well ...............