Police did not name the deceased people and said they were trying to trace their next of kin.
Both craft came from Wycombe Air Park, near High Wycombe, which is also known as Booker Airfield and offers training for new pilots.
A Notice to Airmen was previously issued to warn pilots the air field’s air traffic control services would be closed during three 30-minute periods on selected days between November 7-30 due to a “staff shortage”.
Friday’s crash happened over woods near the historic Waddesdon Manor estate and smoke could be seen rising over the crash site near Waddesdon Hill, according to local media.
RAF Halton, which is about 10 miles away, said no military aircraft had been involved.
A spokesman said: “We can confirm that neither of the aircraft concerned has a connection with either our air force nor the military, and this is as much as we know at this time.”
A spokeswoman for Waddesdon Manor said the crash had not happened on its grounds.
The property is managed by the Rothschild Foundation, a family charitable trust, on behalf of the National Trust, who took over ownership in 1957.
A member of the Rothschild family has told of her shock after a mid-air collision between a helicopter and an aircraft missed her by five minutes.
The woman, who did not want her full name published, said she heard a loud bang while she was driving her car to a dog grooming event, near Waddesdon, in Buckinghamshire.
Just five minutes earlier she had been picking a plant in the Wilderness Woods, the scene of the crash site, on the Waddesdon Estate.
“I’m totally shocked,” she said. “I heard a loud bang, which I thought was a car crash.”
Waddesdon Estate Gardener, Len Bellis, described how he found the “burning wreckage” minutes later.
He had been working nearby when he heard a “horrendous noise” like a tin hangar collapsing.
He said two men came running towards him from the woods shouting, “Did you see it, did you see it?”
Mr Bellis said one of them told him he heard a plane “stuttering” just before the crash.
“I just came across the wreckage,” said Mr Bellis, who described the light aircraft as a “wreck” and “non-existent”, apart from the 5ft burning fuselage.
He said he later found out he was just 10 yards from a body in the undergrowth.
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