That's reassuring. You should be able to apply for a visa waiver at the first port of call. Don't forget to hand it in at the last port in the US or you may get flagged as an overstayer
In some countries cruise companies have special 'group visa' arrangements for shore excursions. I very much doubt if the US, these days, is such a country (it was 30 years ago - I recall visiting Port Everglades under such a scheme. ) but ICBW. P&O should be able to tell you.
I suggest you go to cruisecritic - possibly the most informative cruise site in the world......and look at this link http://boards.cruisecritic.com/forumdisplay.ph p?f=20 which will give you lots of info on New England and what to do ashore by yourself, so you do not take the inflated price cruiseship tour. I would suggest joining the Roll Call too for this cruise but as it is a USA site there may not be very many contributors from the UK....