Just curious to know. So your HKG-LHR flight was delayed by a bit and because of that your missed your LHR - final destination flight? Looks like your transit times were really less..

When you got off at LHR - wasn't someone from CX/BA waiting at the gate to help you transit faster? may be they knew you wouldn't make it and did not bother coming

Good luck with your compensation..No harm in trying