If it were me I would park on the top of Box Hill in the NT car parks (£3 for the day), then you can go down the zig zag and under the subway and pick the route up going up Westhumble Street.
I was completely unaware that the cycleway was actually a loop, I guess I've ridden large parts over the years, but never as a loop. Now I know exactly what those brown signs are for. There are some cracking climbs on the route.