Relax! wrp96 was referencing BA who use both T5 and T3 (as, currently, do AA I believe), you won't have that problem with UA as they only use T2

At LHR terminals 2/3, 4 and 5 are located at significant distances from each other - T4 is outside of the Eastern end of the Southern runway, T5 is at the far Western end of the airport site, between the two runways, and T2/T3 are more or less right in the middle of the airport.

Each has its own vehicle approach and short-stay parking, and if your pick-up driver parks up at the wrong terminal it will probably take them 30 minutes+ to exit the airport, drive round the perimeter and park up at the other location, hence the 'rigidity' of requiring the specific arrival terminal.