PHL-LHR will definitely not be a problem. PHL is my home airport, and I never check bags. Last week I flew PHL-LHR-CPH, and for the first time ever, I got a yellow "put it under the seat" tag attached to my smaller bag from a BA gate agent when I was boarding my LHR-CPH flight. However, I was not asked to gate-check the larger bag (a 20-inch rollaboard that weighed about 14 kg). I was flying CW on the TATL and ET on the short-haul flight, and checked in online for both, bypassing check-in counters. On my return flight last Friday, no one batted an eye on either flight (again ET for the first flight and then an op-up from WT+ to CW for the second).

I have never been asked by BA to gate-check a bag, even when flying short-haul. Then again, I am Gold, so maybe that helps.