I have not heard of such a ticket as you seem to have. "Non-Exchangeable"? Was it a weekend Web fare? Was it from a bucket shop and a consolidator ticket? Did you buy it through BA or from a travel agent or over the internet? Were you not offered some form of insurance when you booked it with BA? How much lower was the fare from a normal discounted "Non-Refundable" but changeable [for a fee] ticket?

While I don't want to pry too much into your personal or business travels, it would be valuable for the rest of us to know what to look out for when being offered such a ticket. Never in my 35 years of buying airline tickets have I come across such a restricted fare.

Please tell us more.