1. Visit the Museum of London & Museum in Docklands
Start with prehistory, end with a look towards the future. While the more contemporary Museum of London galleries are currently closed (the prehistoric, Roman and Mediaeval galleries and Great Fire exhibition remain open), the Museum in Docklands takes up the story complete with atmospheric reconstructions of the London dockside.
2. Read a book
There are plenty of London books around, and time spent in a specialist bookshop is never wasted. But which to read for a relatively brief overview of this immense subject? My suggestion - Roy Porter's London: A Social History succeeds in being both compact and comprehensive.
3. Float down the river
Follow the Thames from Greenwich to Westminster and you'll see the past on its banks, from the Tower of London to the Gherkin. Many boat trips are substantially cheaper if you have an Oyster card.
4. Stroll the Square Mile
The City of London has the markets, alleyways, churches and institutions which drove history. While Westminster governed the country, the Square Mile governed the city's inhabitants.
5. Click these links
Explore London history on wikipedia, Britannia.com, the Museum of London website.
6. Get regal
Visit the Tower of London - built shortly after the Norman conquest, and in royal hands ever since, it's a comprehensive introduction to London's close relationship with the head of state.
7. Walk with a guide
There's nothing like a walking tour for helping you get to know the city. For an overview of its history, there are walks guided by companies such as London Walks; online walking guides like London Footprints; or books of walks, complete with maps and historical information (notably those by Andrew Duncan).
8. Mix and match
Why not read a book on your way into the city, then get an all-day ticket for the Thames Clipper and stop off at the Tower of London? Or follow a visit to the Museum in Docklands with a guided walk?