There was no immediate word on the condition of the pilot or injuries among spectators.
The plane went down today during CarFest at Oulton Park, a motor-racing track about 320 kilometres northwest of London. Photos showed smoke rising from a field near the site.
DJ Chris Evans, who founded CarFest, tweeted that there had been "a serious air incident" and emergency services were at the scene.
Cheshire Police confirmed they were attending an incident at the park.
The event featured an exhibition by the Gnat Display team, which flies vintage Royal Air Force Gnat jets.