I'm not an ICN regular, but happen to have arrived on 3 different flights so far this year, twice into T1 (one of those on BA17) and once into T2.
Generally I'd agree with the above that immigation is a pretty horrific experience. On Sunday evening I arrived into T2 fairly late from TPE and queued for 20 minutes - there were only 16 people ahead of me but a single desk for 'foreigners' and no sign of any interest in opening any more. By the time I was through the line was 40+ people. Arriving on a CX flight into T1 earlier in the month I queued for more than 40 minutes having joined a queue of several hundred being served by 6 desks.
So, I'd certainly go expecting the worst. However, for my BA17 arrival I was first to immigration from the flight and was straight through with no queue at all.
Sadly, although S Koreans can use automated gates at LHR there's no hint of reciprocity...