XV406 started life as a recce trials aircraft with A&AEE/MoD(PE). It was issued to the front line at some point before 1976, to 111: there's photographic evidence of it at Malta on an APC in 1976, wearing the letter D. It also appeared at the 1977 Silver Jubilee royal review, but was wearing tail letter 'M'
My assumption would be that some trial for the EMI pod needed to be carried out before 1977 (hence letter 'D') and probably in 1976 - 2 and 41 both still had Phantoms in 1976; the way the transition from Phantom to Jag was done was to set up a new Jaguar unit and give it the same numberplate as the Phantom squadron - thus we had 2 Squadron, 2 (Designate) Squadron, 41 Squadron and 41 (Designate) Squadron [the same approach had been adopted with the transition of 19 and 92 from Lightning F2A to Phantom, for example] The 'designate' squadron would reach operational capability at a certain date; at 23:59:59 hours that day, the 'old' squadron would disband and the 'designate' unit drop that suffix, so at 00:00:00 hours, the squadron would've re-equipped - at a different location with completely a completely different group of personnel.
My guess is that as there was a declining need for Phantom recce trials, XV406 was issued to 111 Sqn on the presumption that if any trials were required in the closing months of Phantom FBSA/Recce operations, a trials aircraft which had gone onto squadron service would be borrowed to conduct the necessary test(s); the ability to use a 'known' airframe for the tests providing a degree of consistency that could be assumed from previous use rather than wondering whether the randomly-borrowed XV999* from 41 Sqn had any foibles which might affect the outcome of the test being preferred if this were possible to achieve. As I say, a guess, but I don't think it's an unreasonable one.
(*there was no XV999)