Although the traffic is scarce these days, a picture here:
https://www.flightradar24.com/51.48,-0.4/12 is worth a thousand words.
The stabilised criteria need to be achieved by 1000' above field elevation, i.e. 3 NM before the runway threshold (on a typical 3° landing slope that gives 5.2% steepness).
Our understanding to join the ILS "fully" is to acquire its glide-path (vertical) plane as well. That is 10 NM or so for LHR. The capture of the lateral (localizer) signal for the extended centerline better be at least 2 NM prior - that's what pilots need.
However, given the constraints of the airspace (keeping room for corridors of the aircraft departing in various directions) as well as to have enough playground for the ATC who need to make all the various birds walk a nice line in a steady and synchronised pace (speed over ground to achieve and maintain proper in-trail spacing), the aircraft would be actually aligned on the final track at about 15 - 18 NM before touchdown.
At Gatwick with its single runway, there will be departing aircraft in between the landing ones. The cadence of arriving traffic is thus about half of that in Heathrow, and an orderly queue can be arranged within a shorter distance from the field. Which is very desirable for all the other traffic in vicinity.
Keep in mind that planes arriving into and departing from the airport zone will cover one mile every 13 seconds, you cannot ever have too much airspace. For a simple turn into the opposite direction a corridor almost 8 miles wide is the minimum.