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Queen Mary 2 to NY , have your 3 weeks holiday then QM2 back from NY. It wont be inexpensive and it might not give you a full 3weeks over there but in this day and age it is probably your best bet. You could try a passage on merchant freighters but this will need a lot of research and possibly returning from a different port of entry to USA . Travel agents specialising in bespoke travel may be able to arrange but expect arrangements to be complex.
I agree with rum runner that the best option would be to do QE2 from Southampton to New York, then your holiday, and then return back via New York. However, as mentioned, doing that return cruise will be an expensive trip but if you don’t like to fly (and there are lots of people who hate it) it’s your best option. I think the sailing takes 5 days each way and if you check out ‘discover cruises uk’ this shows you all the possible options. There are a number of QE2 transatlantic crossings next year, especially after April 2009, and I’m sure a travel or cruise agent could organise a return trip that would allow you to fit the American holiday in between. The link below shows the QE2 sailings next year.
If this link doesn’t open for you just go to the discover cruises website, go to ‘cruise finder’ and then ‘transatlantic crossings’. Hope this helps.
Oops-noticed that I'd put QE2 when it should have been QM2! You'd struggle to do a cruise on QE2 as it's going to be based in Dubai.