Go onto all your prospective cruise lines and see if they are a non smoking ship. Many cruise lines allow smoking somewhere. All are now non smoking in cabins. But allowing for the fact that most ships are in International waters (Therefore not restricted by U.K laws. } You will probally find that smoking is allowed somewhere. i.e . on open decks. Someone out there will tell me no doubt that such and such cruises are non smoking. I would think that there are not many that are totally non smoking. Wish you luck to find the cruise line that totally bans smoking. You will obviously have to pay a premium price. I look forward to the replies that you will get, be very interested to find out who is totally non smoking! You will be missing out on some great company on open decks. But that is your choice! Good luck and enjoy your cruise.

Many ships have stricty non-smoking, except on a promedade deck.

yes. You could usefully search the rules for each ship/shipping company and in the questions and answers here. Each cruise company has different rules.