Should I ride my first fixie back from the shop (in London)?

You can walk the bike to Bethnel Green overground station and go to Liverpool Street, where you can pick up the circle line round to Monument or Embankment and just pootle over the river. Minimum of cycling, if that's what you want.

Can't take Circle line any time, whether peak hours or not. It's one-a those underground lines.

Crap, can't find the link for the one I'm looking for but I just asked about it, so do a search for TfL bicycle tube map or something.