Governing factors are the airline, time of day (number of flights operated within your time frame), number of check-in positions working and security queues. I was at T3 last Sat morning having arrived a bit late due to a lorry overturning on the entrance road to LHR. Long line for check-in. Had to be pulled to the front of the line due to time of flight. Luckily the security line was not too bad. Still, had to go right to the gate.