Firstly are you travelling from the US to the UK or from the UK to the US? Secondly are you considering taking this wine by plane or having it shipped with a household consignment by sea?
If from the UK to the US by a sea shipment, you are required to declare all alcoholic beverages on your forms. You should always check with the port you plan to have you consignment shipped to as some ports are 100% dry, which means no alochol can be contained in consignments whatsoever. Most ports in the US limit your shipment of alochol to so many ltrs of wine and so many ltrs of the hard stuff. The customs website, the website for your port, and the shipping company are your best sources for information.
I myself cant speak first handedly about this issue because Ive not started packing my household yet, however if you still require info on UK to US shipments in a few months, please ask.
Sorry I cant help at ALL with US to UK shipments.
Sarah