The pilot, who was named as Kevin Whyman by the Heritage Aircraft Trust, operator of the Gnat Display Team, was taking part in an aerial show plummeted to the ground in front of horrified spectators.
The accident happened shortly after 2pm at the CarFest event in Oulton Park, Cheshire, created by TV and radio presenter Chris Evans.
Evans told reporters: "There was a tragic accident, the result of which was that one of the pilots involved in a synchro display lost his life."
The visibly-upset presenter added: "Our condolences go out to his family who have been informed.
"The police have also advised us that the best thing and the safest thing to do is to carry on with the event bearing in mind that there are 10,000 children here - and that is what we are going to do."
He said it would be "completely inappropriate" to speculate on how the accident happened. Evans said he would give a tribute to the pilot at a later point.
An Air Accidents Investigation Branch (AAIB) spokesman said: "AAIB will be investigating and is sending a team to the site."
CarFest said in a statement: "An aircraft flying with the Gnat Display Team came down approximately one mile north of the site. The pilot has been confirmed as a fatality. We do not believe that any other person has been harmed in the incident.
"We are working very closely with the police, emergency services and all relevant authorities. We have helpfully received images and footage captured by those close to the site, which will aid with the police investigation.
"Should anyone else have similar photo or video footage, they are asked to keep hold of it in case the authorities request further information.
"Our thoughts are with the family of the pilot and all those affected at this time."
Evans had first tweeted that there had been a serious air incident at and that emergency services were in attendance.
Eyewitnesses described horrified spectators screaming as a plane nose dived suddenly during a display.
CarFest is described on its Twitter profile as Evans's "dream of the perfect family festival", featuring cars, planes and music. It is raising money for BBC Children In Need.
The event in Cheshire began yesterday and is due to finish tomorrow.
A second event is due to take place at Laverstoke Park Farm in Hampshire between August 28-30.
Onlooker Johnathan Randall tweeted: "Think I've just witnessed a plane crash? Crowd looks glum, confused, concerned. Everyone on their phones."
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