tired....
...to re-iterate what has already been pointed out here, this gets an airing regularly.
The problem that HD and colleagues have with LHR is the interaction with the helicopters (and other fixed wing flights) in the LCTR.
HD/120.4 et al can tell lots of stories of aircraft decending below the GP causing major incidents. This is particularly true when LHR are on 27L/R and LCY is on 10. Things are so finely balanced in that configuration.
Whilst we would love to say cleared ILS and 'forget' you we can't. Even if MATS pt 1 was ammended, I doubt that the local procedures (MATS part 2) would change.
There is too much going on below you!