Is your $47k inclusive of VAT?
You may be missing some extra costs between the US and the UK. It may be possible to ship a machine from the east coast of the US for $2000 but don't forget it is going to cost something to get the machine to the eastcoast in the first place. Also I think the crating is more complex for export machines, machines for delivery in North America are just palletized and wrapped in plastic not fully crated.
I think if you did get firm figures on buying a machine in the US and having it shipped you might find your landed cost in the UK plus local delivery will come out a lot closer to $47k than $31k.
Not that I don't have sympathy for you. I have visited the UK frequently for business and pleasure and have seen how prices of many things are much higher over there.