RC Dad, you will need to contact a freight forwarder in your area to arrange that type of transportation, they will have the experience and contacts with several airline and ship lines to choose from.
From previous experience in shipping large production equipment from Japan to the US, I know that airfreight would be very expensive. If you have time and shipping your RV to US is really what you would like to do, then ocean frieght would be a much cheaper route.
What type of RV are you planning on transporting? Is it a trailer or motorhome? Are you planning on using it here for a while then returning it to the UK? It may be cheaper to rent an RV here and not have to bother with import/export issues.
I would think that if you bring a motor vehicle from overseas, that it would have to comply with US Dept. of Transportation regulations. A knowledgable freight forwarder would know the answers to all of these questions.
Hope this helps.
Duane