I have just seen this thread and am astounded that BA is claiming you did not have a ticket so could not be denied boarding. You had a reservation as evidenced by the PNR that BA failed to ticket and failed to take payment. That is BA's fault not the customer’s. You even selected seats and tried to check in online and actually got to LHR. If BA hadn't made a commercial decision to remove ticketing services at the airport they could have issued one to you. I personally can see why you feel you don't want to pursue this but I think you should. At the very least get the deadlock letter and then decide.