Hi,
The E-3 can only carry out training approaches at airfields that have a crash cat the equivalent of Military 3A or 4 (depending on crew on board). These are becoming quite rare in the RAF with base closures.
The E-3s have been going to 'civvie' airfields for years for training instrument approaches (particularly NDB and VOR/DME). Cost is critical however so they go to whoever gives the best deal. This has usually been Newcastle, E.Midlands and Prestwick in the recent past, but can sometimes be down to a negotiation on the phone between the Capt and ATC on the day.