National Maritime Museum, Greenwich
Originally the Greenwich Hospital, which then meant a retirement home for sailors of the Royal Navy, it was built in 1692. It became the school for naval doctors, then in 1934 it was given over to the Maritime Museum in Greenwich due to its location as a ship landing since the Roman times.
The Arrival - Greenwich DLR station
The DLR system is all over South and east London, and runs really well. Being automated, it's not as affected by strikes, which made it ideal for my last visit during a pile of labor actions.
You disembark in the center of Greenwich at the Cutty Sark stop, and this is just a delightful and very eclectic area of shops, dining and inns, plus a serious history on naval and astronomic usages. Walk east through the town to the museum, it's hard to miss and signs abound.
When you enter, you find you don't have to pay a cent to visit. Primarily self-guided, but they do have timed tours. There is also an extra fee to see area of special exhibitions, but I was in a bit of a time crunch that day.
As you go through the other floors, you see the massive center shipping world play area, and surrounding it more displays of naval history (as well, this is what made England the maritime power it is).
And there is quite a bit to the great battle of Trafalgar where the fate of England truly was held in the balance, and how Lord Horatio Nelson saved the day highly outnumbered.
Old timey sailing and the age of wooden ships and iron men isn't for everyone, but wow is this one hell of a collection of old items. Also the Cutty Sark (the world famous clipper ship) isn't far from here either. I found it very interesting with the history and the place this holds in the English DNA.