Both - I used to do that and my (not ideal) route was this:
Balham
Clapham South
Across Clapham Comon to the top of Cedars Road
Down Cedars then right onto Wandsworth Road
Up to Vauxhall
Across at Vauxhall and follow river southside to Westminster Bridge
Right onto whatever the road's called that runs north along the river
Left up Northumberland Ave. to Traf. Sq.
Up Charing X Rd
Illegal right turn onto Shaftesbury
Back roads up to the bit of UCL near KX, passing Russel Square
Both - I used to do that and my (not ideal) route was this:
Balham
Clapham South
Across Clapham Comon to the top of Cedars Road
Down Cedars then right onto Wandsworth Road
Up to Vauxhall
Across at Vauxhall and follow river southside to Westminster Bridge
Right onto whatever the road's called that runs north along the river
Left up Northumberland Ave. to Traf. Sq.
Up Charing X Rd
Illegal right turn onto Shaftesbury
Back roads up to the bit of UCL near KX, passing Russel Square