The Tower of London needs at least a day on it's own, and it's expensive to get into - won't be worth spending the money if you are only there for an hour or so. Although I seem to recall that they have changed the rules on charging admission to UK museums - I may be wrong here, so check up first.

The cabinet rooms are difficult to get into and there's usually a queue.

Don't bother changing money before you leave: definitely DON'T change money at an airport moneychanger. Just take your normal bank pass and PIN for money out of the wall on arrival in London. If you do this, although you will pay the transaction fee (unknown for your bank), you will get the Inter-bank rate for your money, which is more favourable than the tourist rates. If you get out a decent chunk of money this will be the cheapest overall.

I know I don't sound positive here, I am just warning you about delays on a short timetable.