orojim, how did you handle the important document return with USPS? Were they able to provide a pre-paid envelope?
I'm afraid that I took the path of least resistance: I just had the materials returned to me by low-speed Royal Mail, signature required. That's what the UKM Guide booklet said would be used for anyone who didn't make other courier arrangements. USPS was fine going USA-to-Liverpool, but couldn't set up the return.
I think those other arrangements would be very easy for someone in the UK, as they could arrange everything in both directions with a domestic courier or Royal Mail. Here in the USA, I went to offices of both FedEx and UPS to inquire, and got no joy from either. Some commenters here have mentioned opening an account and setting up a return that way, but by the time I was ready to submit, I just wanted to start the process.
So while I paid no money for the return of documents, I did spend some extra nail-biting time. The approval letter was written on January 9 and delivered to me on January 24. All documents were returned with the letter.