I've always been processed very fast, but I have never been on a flight arriving at the same time as another flight. If that LHR 777 gets in on time, half its pax could be off before I get out. I am an extremely fast walker and have no doubt that I'll be the first from my flight to reach Immigration, but those other people will be in my way.
No offense to any of you who may be traveling on the 9:55 a.m. departure from LHR on Jan 2, but here's wishing you a nice long mechanical delay in LHR or a inoperative jetway at JFK!