Sue Crawford lives near the crash site and heard it from inside her house.
“It was almost like something dropping several times, like dustbin lids or dustbins being bashed.. we weren’t sure what we were hearing. But now we realise what it was,” she said.
Ms Crawford, who said she also lost somebody who was serving in the RAF a few years ago, has been to the scene to pay her respects.
“We realise as a family, how awful it is when something like this happens. Especially at this time and when they were involved with something so special like the VE [Victory in Europe] day celebrations.”
Another woman, who laid flowers at RAF Coningsby’s perimeter fence, said: “We all love coming out here to watch the planes.
“We can see them all the time, so it will be a sad day for everybody.”
The MoD said that the pilot’s family had been informed and asked that their privacy be respected “at this difficult time”.
RAF enthusiasts had gathered to watch the planes on Saturday.
Speaking to the BBC, Sam Butler said: “They are well known to local people round here – they are treated like one big family from people who come here.”
Andrew Backhouse, who had watched the Spitfire fly overhead, added: “He was one of the best of the fleet…. Our thoughts go out to him. I’m sure the truth will come out eventually as to what happened.”
Lincolnshire Police said on Saturday it was a single-occupant aircraft and nobody else was involved.
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