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There are e-gates for UK passport holders, but I'm guessing a child was involved. If they were the only passengers caught by this then it gets very difficult to argue with BA. GroundForce have a habit of closing the gate before the advertised 20 minutes so if they were there before then they have a stronger argument. If it happens again, best to send one adult through the e-gates to plead with the gate staff to hold on for a bit. Otherwise it is the responsibility of passengers to be at the gate in time, no getting around that.