Jonwo is right, that the non profit shows in London are bought over to America via an indipendent producer.
I don't think it is commercially vialbe for a show to go to to London via its American non profit theatre. Keep in mind that on Broadway if a non profit show transfers to a commercial run it is because a Broadway producer wishes to do so. Yes, 39 steps is still playing on Broadway but it is no longer produced by Roundabout. Once it left The American Airlines theatre and moved to the cort it had a different producer.
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll