Rotherhithe tunnel?

I tried doing Rotherhite once, on the road; it was generally a bad experience. Plus you're not allowed through there on a 125cc moped (for your own safety IMHO), so doing it lone wolf on a bicycle probably wasn't/isn't too great an idea, a group rolling through there would probably be ok.

I live in Brockley (just up Loampit Vale from 'Sham Station) and my old man lives in Bethnal, and I do this journey fairly often. The route I usually take is:
Victoria Park (Approach Rd entrance) » Mile End » Burdett Rd » Canary Wharf » Westferry Rd » Greenwich Foot Tunnel » Greenwich High Rd » Brookmill Rd » A few more little streets (No, I'm not going to direct you to my door, though you are welcome to pop in for a cuppa via PM request) » Home!
That usually takes me 15-20 mins, traffic is generally OK and the roads aren't too bad (except for the odd bit of nasty on Burdett Rd).

tl;dr