Kind of need a bit more info really! What sort of things do you like generally, shopping, museums, galleries, art, food, history? Do you come to London often or is this very much a one-off? Do you want to do sight-seeing or just have a general treat/day out? General budget?
As the weather is of course quite variable my itinerary would be very much indoor based at this time of year, the parks are lovely and in summer there's nothing better than a stroll along the south bank but in December I wouldn't count on it. There's also lots of brilliant free stuff to do in London but then again I could very easily spend hundreds in a day if I had them available!
Here's what I would personally do on a mid-range budget for the day:
Depending on what time you get in I would have a nice coffee or brunch in the vicinity of St Pancras, Granary Square is lovely or if pushing the boat out there is the champagne bar actually at St Pancras or some nice options at the St Pancras Renaissance hotel which is a gorgeous gothic building right next door to the station.
Then weather allowing I'd stroll down towards the west end (or if bad weather hop on the Northern or Piccadilly for a couple of stops to Leicester Square or Covent Garden) - possibly calling in at a museum en route. The British Library, British Museum, the Sir John Soames, the Foundling Museum and the Transport Museum are all on your route, my personal favourite is the Wellcome Collection which is a small science/medicine museum which always has some very interesting exhibits (slightly not on your route as it's about a 15 min walk up the not very attractive Euston Road with heavy traffic thundering past though, if that matters to you). Or if art is more your thing then I'd do the National Gallery or National Portrait Gallery which are both very near Leicester Square.
Or if shopping is more your bag wander around the nice small shops in Covent Garden and watch the street performers (or if time do both).
Then I would go for a matinee (or an evening show) at one of the West End theatres. If you fancy a last minute experience you can queue at the booths in Leicester Square for last-minute discount tickets but equally if pushing the boat out buy the best seats in the house for whatever takes your fancy.
If time before or after the show I always make time for a browse in the excellent second hand bookshops on the Charing Cross road just up from Leicester Square stations which are always a treasure trove. Then again depending on timings I'd go for a chinese meal in Chinatown before or after the theatre. If I didn't need to rush back for a train I'd have a cocktail or two somewhere in the west end before heading back on the tube to St Pancras.
But like I say that's very much my own choices and obviously doesn't include much sightseeing and leaves out Oxford Street entirely, if this is your one and only chance to see London and you wanted to do Tower of London and Buckingham Palace and the London Eye and such, or if you wanted to blitz your christmas shopping at the big department stores then we could put together a totally different itinerary for you!