The easy answer is no it's not worth it. I am assuming you are coming from the States and your flight arrives on time; you will take between 1 and 2 hours to deplane and clear immigration. The baggage storage facilities close at 11 pm so you will most likely be out of luck there. If you were lucky and able to make the storage before it closed, it would cost £11 per piece for overnight. Then add the cost of getting into and out of central London, the cost of a meal for two, if you could find somewhere to eat. The wear and tear on your body and nerves. Nope - I'd head for a comfortable bed and a decent nights sleep!
Edit. Check out this web site hot-dinners.com for a list of late night restaurants in central London. Will give you an idea of what is considered late in London. There are a couple of 24 hours places.