Communications were re-established and the aircraft was safely escorted to Cardiff Airport, a spokesman added.
The Challenger 300 jet left the airport at 19:20 GMT, thought to be heading to its original destination, Dublin.
Cardiff Airport said the plane had temporarily lost radio contact.
All the main emergency services sent crews to Cardiff Airport at about 16:30 BST, including seven fire appliances. Police and ambulance also attended.
The sonic boom caused by the RAF jets was heard across Oxfordshire.
Source: BBC NEWS
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