The Canaries is usually warm in December /January and it's not too far to travel for one week as long as you fly out. Don't be tempted to sail to the Canaries at that time of the year as it takes a couple of days usually to get there and the weather is usually pants. Sometimes the Bay of Biscay can be awful and by the time that you get there you don't have a great dal of time to enjoy the sun before you have to return home.Given a choice I would plump for the Caribbean too but we found that seven days is really too short to fly there and back and have a really relaxing time in between. Still if you have to settle for a week then there are some good offers on as Wilba says.
Caribbean is the nearest warmest in Jan. Plenty of cruises to choose from.
I can recommend Thomson's Red Sea cruise, the weather is good, the cost is very reasonable particularly if you book late, flights are available from a wide range of UK airports, the tours are memorable (Petra should not be missed). The food, service and entertainment are very good considering the cost of the cruise.