Personally, I would rebook the hotel to one out near the airport and just catch a good night’s sleep. Then again, I’m old and like to take it easy, especially at what looks like the tail end of a longer trip...
The problem is that when you land at 4PM, assuming you are on time (big assumption, especially at that time of the day), taxi to the gete, get off the plane, customs (depending on where you are flying in from), luggage pickup, etc plus the trip into London during rush hour, could take 2-3 hours just to get to your hotel. At that point, attractions like museums, tower, even the London eye will be closed. If the weather is decent, perhaps a walk on the South banks of the Thames would be a good use of the remaining daylight. If you don’t feel like walking, take the river boat out to Greenwich and back. Grab some food, or if you are really ambitious you could consider taking in a show in the Theater district.
In any event, if your flight leaves at 10AM, you’ll probably want to shoot for leaving to the airport at 7AM at the latest since you will again be facing rush hour traffic (though for the most part “against traffic”), so you may not get that much sleep.