There was certainly a Vampire being used for engineering training at Brooklands College around 1992, I assume this must have been XJ772, I remember doing a few bits on it.
The Vampire was replaced the following year with a Jet Provost so I guess this must have been when XJ772 was moved to the De Havilland Heritage Centre.
I'll confirm the registration if I can find my apprenticeship notes. (Yes, sadly after almost 30 years I've still got them !)