I ride from Nunhead to Canary Wharf. The Greenwich tunnel is definitely the way to go - slightly a pain waiting for the lift and then walking, but it's really not that much of a bother. I have a friend who used to ride through the Rotherhithe tunnel, but that would be horrible. It's a long way out of the way to go up to E&C. I have a fairly direct route from the south of Nunhead to Greenwich which avoids most of the main roads, but it takes some planning because there are no proper cycle paths. I ride down St Norbert Road to Brockely, then Malpas Road (can be a bit busy, but not terrible), Florence Road, Herald Street, Tanner's Hill, brings you out to New Cross Road, which is busy and requires some care. Left onto Deptford Church Street (it's wide so generally ok) and then right at the first roundabout around Creekside then Copperas (the building works there are now a bit of a pain, but ok). Then you can either turn right along Creek Rd to Greenwich (busier) or when I started riding there I would go straight across the pedestrian crossing and onto the path along the Thames, which leads to the tunnel at Greenwich. This works out pretty well with the only really messy bit being New Cross Road. Depending on where you are in ED you won't want to ride up the hill to join my route from the start, but you can probably pick out a route across Peckham Rye Common, through the backstreets of Nunhead (avoiding Evelina Road), and over to Brockely. Good luck - don't be put off - I love cycling in London.