A video of the crash shared on social media on Wednesday appeared to show the two pilots ejecting from the aircraft before it nosedives and crashes in flames.
The footage shows a plume of smoke and fire erupting as the aircraft hits the ground, appearing to narrowly miss homes.
In a statement on social media, the RAF said: “Both pilots are doing well, they are in extremely good spirits and expected to make a full recovery.
“A formal investigation into the circumstances surrounding the incident is now under way and, as a precautionary measure, the RAF has temporarily paused Hawk T1 and Hawk T2 flying operations.”
The Hawk T1, and newer T2 versions are transonic, two-seat training aircrafts used to train fast jet pilots.
The Red Arrows, based at RAF Waddington in Lincolnshire, are included in the pause, however they were not due to fly again until Le Touquet Airshow in France this weekend in any event. It is not known when the restriction will be lifted.
