I don't know this route, but wouldn't it be quicker to use the road?
I take it you're talking about Clapham Common. Refer to map -
Streetmap.co.uk- search results(Sorry, the link thingy doesn't seem to work with Macs)
I only use this path northbound because of the 1-way sytstem near CC tube station. The path runs from Narbonne Ave to the SE of the Common, past Eagle Pond, L+R across Windmill Drive, then due N to Cedars Road. I need to go from Cavendish Rd to Clapham Common Northside, by Trinity Hospice, to get home directly and avoid unnecessary A-roads.
Not using the Common path, i would have to:
1. Carry on along The Avenue - part of the South Circular - and then make a right turn across N lanes of traffic onto the A3
or
2. Turn R at the end of Cavendish Rd onto Southside and then past the tube station, down a hill, then L up a hill to get home.
I can't turn left from Southside anywhere on this map north of Clapham South tube, except to use the cycle path, due to poxy 1-way systems.
Both of these are longer, more dangerous, less pleasant and slower than using the cycle path.