-
At the moment I’m going past Lambeth North from Elephant and then crossing Westminster Bridge. Doing that to get to Birdcage Walk seems to take about 20 mins
For variety you could go Lambeth Walk and Lambeth Bridge then either Horseferry, and round Victoria (playing with traffic) or Embankment Sloane Square-ish. Basically head to Hyde Park, then through the Park.
Doubt these will be quicker but variety is the Spice of Life.
Or, go the other way and hit Waterloo Bridge, through Covent Garden then Bloomsbury and Marylebone.
What route are you taking atm? CS6 from E&C to Blackfriars and then CS3 from Blackfriars onwards is a nice route.