The RAE was established at Bedford in 1946, but I haven't found a crest other than the one you posted, which could not have been taken in 1962 as you can clearly see the red/white/blue 'raspberry ripple' livery worn by this aircraft that wasn't devised until 1976.
The Gnat was first built by Folland Aircraft Ltd in September 1962. This example (XP505) was later used for research into turbulance and air movement by the Royal Aircraft Establishment (RAE) in Bedford, Bedfordshire, between 1970 and 1983 and this aircraft survives today in this colours with the Science Museum outstation at Wroughton, Wilts.