If you're going from the Uk then the southern parts of Spain are popular choices. It only takes 2 or 3 hours to reach most destinations, and if you go for a southern island like Gran Canaria it's usually quite warm (for example, the temperature there on this January day is 18 degrees celsius.)
If you just want generally better weather than in the UK, the South of France is also often nice in the winter, but if you want a real sun holiday you have to go properly south - if not southern Spain then further. A lot of nice places are still affordable even if the flight takes a little longer - have you thought about Malta, for instance, or Greece? (though you have to check winter weather conditions carefully - for instance, Crete is a long way south but the winters aren't specially warm.)
You can find a list of suggested winter destinations here (lower down on the right of the page) but I would also suggest consulting a travel agent.