I must admit it would not be a primary reason for joining a cruise ship, but have been on 16 so far and none of these had a 24 hrs coffee service to the best of my knowledge, but perhaps someone else will respond.
Princess ships have 24hour coffee and tea available in the Horizon Court buffet area, some of their ships do cruises out of Southampton in the summer.
P&O have buffet areas open 24hours.
NCL Jade sails from Southampton in the summer months and has a 24hr restaurant called Blue Lagoon.
Thomson is indeed 24 hours.
Hi, I was on the Independence of the Seas in august and they have now installed kettles with coffee/tea in the cabins. Enjouy ur cruise.