How far do you want to run? I'm currently temporarily staying in central Covent Garden and so have been trying to discover suitable routes.
So, running down to Waterloo bridge, crossing it, heading east to the Tate Modern / Globe is 1.5 miles. Then from there you can double back and run back the other way, past London Eye and Westminster, cross the bridge there and either run back along the Embankment to emerge at the north side of Waterloo Bridge or carry on running the other way to Battersea bridge. If you're running early in the morning, watch out for iciness on the paths by the river. Oh, and during rush hours and during the day at weekends there's a real bottleneck on the path around Blackfriars station as everyone is funnelled into a sort of tunnel.
Heading north rather than south, you can run from central Covent Garden to Oxford Street (only one for early mornings, this one - too many tourists otherwise) then up Portland Place to Regent's Park, one lap of the outer circle then back to Covent Garden through Bloomsbury and it's just over six miles. I extended that run to 15 miles at the weekend by adding another lap of the park and then joining the canal path (cross the little bridge by the zoo entrance) and running to Little Venice and back (two miles each way) before running back through the Park and then Great Portland Street and Bloomsbury. Regent's canal path is great but I don't know if it's lit at night so I've only tried it during daytime?