Not surprisingly the revised plans for how to waste £30bn now show an orbital route closer to the centre of London which barely crosses the river:
http://londonist.com/2014/05/plans-for-a...london.php

It doesn't even reach down to Clapham where the A3, A205, A24 all converge.

This removes all plans to remove traffic from the south circular and provides a tunnel along the southern bank of the Thames, one of the quietest routes above ground. Still it will help those developers in Battersea who are getting a new underground line for their few residents.