There are shower facilities in the Admirals Club lounge in the same terminal that you arrive. It's right before you exit the gate area on the left hand side. Look for the signs.

I've used them before although I was out partying in Munich the night before and had a hangover so any shower looked good to me.

Since you have such a long layover, you may want to head out to London city center for a visit. It's only 15 mins via train.