text: Kevin Whyman, 39, was killed in the crash at Oulton Park, Cheshire, at about 14:00 BST on Saturday.
  But TV and radio presenter Chris Evans, who created the event, said police had advised it would be best to carry on.
  A minute's silence has been held at the festival site and visitors stopped to pay their respects.
  Mr Evans said the crash in which Mr Whyman was killed was a "tragic accident".
  A visibly upset Evans told reporters: "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."
  CarFest organisers said the festival had resumed but there would be no further aerial displays.
  Mr Whyman, nicknamed "Jester", was a member of the Gnat Display Team and married with a young daughter.
  In a statement, Heritage Aircraft Trust, which runs the team, said: "Kevin was a Royal Air Force-trained fast jet pilot whose enthusiasm for flying the Folland Gnat was infectious.
  "He will be greatly missed by his family, the team and many friends.
  "Kevin leaves a wife and young daughter. Please respect the privacy of family members and of the team at this most difficult time."
  Shocked spectators fell silent as the plane suddenly nosedived during the display, before disappearing behind trees.
  Moments later a plume of thick black smoke billowed in to the sky.
  BBC producer Justin Bones, at the scene, said two planes had performed a low-level, close-proximity pass just before the crash.
  One of the aircraft had failed to pull up and crashed north of the circuit, he said.
  Mr Whyman, who started flying the Folland Gnat in 2005, was one of the founder members of the display team in 2007.
  He lived in Westminster, central London, and split his leisure time between the airfield during the summer months and the ski slopes of the Swiss Alps during the winter.
  An Air Accidents Investigation Branch (AAIB) spokesman said it would be investigating the incident and sending a team to the site.
  Cheshire Police is also investigating.
  Mr Whyman, who was born in Chester, was a Cambridge University economics graduate.
  He trained with the university's boat club and coxed Cambridge to victory in the 1996 and 1997 boat races against Oxford.
  He had a career with the RAF from 1998 to 2001, when he left for a trading job with a US investment bank in the City of London.
  He completed his civilian flying licences so that he could continue to fly.
  Evans is a car enthusiast and was recently named as the new presenter of the BBC's Top Gear show.
  CarFest is described on its Twitter profile as his "dream of the perfect family festival", featuring cars, planes and music while raising money for BBC Children In Need.
  The weekend event in Cheshire began on Friday and a second festival is due to be held in Hampshire later this month.
target: The CarFest motoring event has resumed, a day after the death of a pilot whose aircraft plummeted from the sky during an aerial display.