Is UK National Cycle Network Route 20 fully open and fully signed all the way from Wandsworth (in London) to Brighton?
While the sustrans website can get a little behind, they're normally pretty prompt to announce route openings. And they say it isn't yet. But you should be able to plan a route to link the sections that are open -- after all, much of it is planned to be on road anyway.
Even with a signposted route it's unwise to rely on the signs, especially in urban areas. The signs are small and easily missed if you're concentrating on the traffic. I've been caught out by this on NCR4. So I suggest spending some time with maps first (cyclestreets, Google, or paper). Cyclestreets shows gaps in the route, and doesn't use all of what does exist; this is based on openstreetmap data which I would expect to be reasonably up to date on a major bike route.