It's an unfortunate outcome since BA is the judge of circumstance and presumably you didn't call BA at the point you knew you were going to be late. Plus the deadline for conformance is 35 minutes, so I am guessing you were trying to check in luggage. If you had edited your baggage and taken it through main security then this would get you on the booking. Having offered WTP as a Plan B, you probably exhausted your goodwill in turning it down. I don't enjoy saying this so I hope a supervisor can help to recover something here.