Carried out some more testing.
As I was flying the FBW A-320 in my post above, I thought I'd try the Asobo A-320.
Flew a 09L App - No ILS, as soon as I was at the 27 end, the ILS came alive. Did a 180, still had 27 ILS. Passed over EGLL, lost ILS.
Flew to EGKK (freeware airport) flew a 26R App - good ILS all the way - I-WW. Passed EGKK - 08R ILS came alive I-GG.
I then followed xChris93's instructions and then removed all my addons except your EGLL airport.
I then repeated my tests exactly the same with exactly the same results.