We were on K&L over Christmas (2008)--long coats/gloves hid everything else! But for the theatre night and the dinner night in Paris we dressed up a bit, and I brought a dress shirt and tie, with a Christmas sweater. Frankly I didn't notice a lot of fancy wear by the locals at the theatre.
The London Eye was great--we were surprised with tickets to it by our guides, so I'm glad I didn't pre-purchase. Not sure if they still do that, though--I'd try to get the tickets in advance to avoid a long line.
There are Oyster Cards for tube use--load up the card, discounted tube rides, etc. I overloaded mine and to this day am not sure what the best approach to it is (re the amount to put on it). You'll have some free time in London but not alot, so I'd plan to walk to things from the hotel.
We loved our time at DLP (Christmas Day with
ABD and then a post-trip add-on)--but the rides were much more intense (the roller coaster rides) than those in the states! Are you staying at the Hilton Arc de T? If so--easy walk to the Arc--go there at night and go up to its top (cool little museum up top, and the view from the roof is great!) There is also a great public park nearby--if time, definately worth a stroll.
Great trip!