You mean "Minis" not MINIS (upper case is for the new car).
There are several distributors who can bring in complete cars. The first I can think of is Turky's in Charleston, SC. There is/was also The Mini Farm somewhere in Georgia. Mike Ehrlich in Long Island knows a couple of builders in the U.K. who could put a car together for you but I don't know if he's brought in complete cars. Since you're in NY you could also contact Doug at Mini City and see what he can hook you up with.
Out of curiosity, why a U.K. Mini? There are quite a number of Minis already here. If you want a roll-up window car, there are plenty of Canadian Mk3 and later Minis in the U.S. I'd stay away from the later fuel injected Minis as they 1) don't legally meet the age requirement and 2) there is no real support for them in the U.S.