Here you go:
https://maps.google.co.uk/maps/ms?msid=2...1,0.134754
Google was being a bit glitchy but the link should hopefully work
I used to do this route everyday when I worked in soho. It's by the far the best way there in my opinion (and I've tried lots of routes). It's not the fastest (but it's by no means indirect) but it is the most picturesque, interesting and safe.
It's essentially one green space after another for the first 5 miles Camberwell New Cemetery, Peckham Rye, Surrey Canal Path, Burgess Park much of it along paths or along cycle paths and crucially it doesn't include Old Kent Road or Elephant and Castle roundabout.
Then when you get towards the Elephant and Castle area (half way) you get to see some lovely sights Waterloo Bridge is stunning, then Covent Garden, past Leicester Square, through Chinatown over cobbles (lovely in January when the lanterns are out) and then bomb it down Wardour St through the heart of Soho it's like a tour of London that you'd normally have to pay for.
The only slightly hairy bit is Waterloo IMAX roundabout (but that's all cycle path now) and Wardour Street (pedestrians everywhere)
I couldn't recommend the route enough. Enjoy.