I cruise as a single person all the time with P&O. There should be no problems, the cruise line will try to accommodate any requests you have. Any cabin either inside or out is more than adequate/comfortable for a single person.
When Dining I would recommend that you ask to be seated at a table of 6 or 8 persons, more people to get to know and talk to.
As for on board activities, they do have singles get togethers, but these are not obligatory.
So really it's up to you.
Hi, i have been one quite a few cruises on my own, i find thomsons very good as they have a solo meeting on the first day at sea and there are quite a lot of passengers on there own, if you like me i tend to make friends easy, also i went on the marco polo last year and they did the same and they have dance hosts which was good and even lessons.
Princess and P&O are both very geared towards singles. They have 'Singles Mingles' get togethers throughout the cruise fo you to meet other single people travelling. At dinner they normally seat you with tables of around eight people from two or three families, so there is plenty of opportunity to make new friends.