Air crash investigators were called to the crash site, which usually only happens for light aircraft incidents when fatalities have occurred.
Both aircraft had taken off from nearby Wycombe Air Park, a spokesman said.
The plane in the crash is understood to be a Cessna 152.
The crash site is near, but not in the grounds of Waddesdon Manor. The airspace is commonly used by pilots for training exercises.
RAF Halton, which is around 10 miles away, said no military aircraft were involved.
Officers say the first priority is "preservation of life". She said all visitors were safe. "Everyone is helping the emergency services".
The Air Accidents Investigation Branch said Friday it was sending a team to Aylesbury, Buckinghamshire to investigate.
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"We sent a number of resources to the scene, including the Thames Valley air ambulance, two ambulance crews, two ambulance officers and a rapid response vehicle", said a spokeswoman.
Buckinghamshire Fire and Rescue Service said they now have seven vehicles responding to the incident, including fire engines as well as urban search and rescue vehicles.
A Notice to Airmen was previously issued to warn pilots the Wycombe Air Park'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".
"There were a number of road closures following the incident which have now been lifted".
Emergency services rushed to the scene close to the village of Waddesdon following reports of an incident at 12.06pm.
A police cordon is in place outside the entrance to the Waddesdon estate.