I do this trip routinely. If not flying direct I can recommend connecting through DFW. It’s a nice length of flight from LHR, an easy connection experience (well as easy as the USA can offer for INT-DOM connections) and there are plenty of onward flights into MSY (which is just over an hour flight time away from DFW).
Only downside I can see is that BA don’t use any newer aircraft into DFW...however I usually opt for J direct on BA or F via DFW on AA’s 77W if the price is right.