AA used to fly BNA-LGW but it did not work unfortunately. However once capacity is sorted out at LHR/LGW I hope to see it return.

Anyway I would go via DFW or MIA they make most sense geographically as well as ATL. However with ATL you would have to fly DL BNA-ATL which means if you missed your connection it would be your problem as BA and DL are not partners unlike AA and BA.

My recommendation.

AA BNA-MIA
BA MIA-LHR