but the how does the controller obtain the distance?
by adding up the spacing requirement between each inbound and adding a bit extra for the 'catch up' (as aircraft slow from from 210-160kts)
e.g You are number 4, no.2 is at 10 miles 2x six mile gaps plus a couple for the catch up, you are 14 miles behind no.2 or 24 miles from touchdown.
If the spacing is minimum vortex (ie no departure gaps required) a good rule of thumb is to add up in fives e.g you are no.5, no.2 is at ten miles therefore you have 25 miles from touchdown.
In light traffic conditions an approximation of the intended track is used.
e.g passing abeam the field, you may have a 12 mile downwind, 4 mile base leg and an 8 mile final or 24 miles from touchdown.
Hope that's clear enough, it's always a 'best guess' but they are surprisingly accurate.
Out of interest, do you always get told your track miles at Gatwick ?