I have never been on the Black Prince but I am sure it is pretty universal on all ships that you are welcome to stay on board when in port. We did this a few times, sometimes getting off the boat, having a wander around the town and then popping back or not getting off a all. For us we enjoyed the extra space and peace you get when most people are off the boat. It is a chance to relax as excursion days can be exhausting. The shops were not open but the bars and restaurents were. Often the veiw from the boat is lovely and it gives you chance to fully explore all the facilities. We plan to treat ourselves to a spa day this time.
I have cruised many times on this ship and would confirm that there is no pressure to get off the ship at any port of call. Many people thoroughly enjoy having "their" ship virtually to themselves on port days. There are normally some activities on these days too and, of course, the restaurants are fully operational. I hope you have a lovely cruise.
Thank you very much for answering my mail. this has eased my mind quite a lot, as my husband has been in hospital and we did not wish to cancel our holiday. Thank you again