Jolyon Palmer, a racing car driver who competes in the Formula One feeder GP2 series, said Mr Barnes saved his life in 2007.
He tweeted: "Helicopter pilot Pete Barnes helped save my life in 2007 after I had a serious quad bike accident. Extremely sad news today."
UK HEMS, the charitable collaboration of UK helicopter air ambulance services, said Mr Barnes was a hugely skilled pilot.
The organisation tweeted: "Thoughts are with family and friends of Capt. Pete Barnes. A hugely skilled and experienced former HEMS pilot."