Hi Andy,
The cycle route switches sides without much thought behind it, from east to west the cyclist has to turn up off of the towpath and walk along the narrow pavement of the bridge up the road. There is no marked crossing and then you're back on the cycle route. Even though its crossing a fairly busy road it's still preferable to the narrow overgrown path on the south side of Brookwood lye where I believe there's no cycling.

 I'm nearby here so if you want any more info on this or somewhere in the area let me know. I think that a few of the "cycle routes" in woking are really just places where you could cycle if you want but there's no real comprehensive infrastructure beyond some disjointed paths and gutters - as for the Basingstoke canal there are a couple of points like this which I've cycled past but it's mostly continuous. 