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That looks like the Downs Link with a bit added from SW London to get you to Guildford, right? I've done that a few times - it's pretty flat and straight (and drama free, though there's a potential hike-a-bike short section somewhere south of Horsham IIRC) and you'll end up in Shoreham-by-Sea. The extra distance to Brighton runs through the port and along the seafront.
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By the sounds of it, I've done it on two different rides.
The first bit out to Guildford is decent, but spends a bit much time on tow paths for me.
The Downs Link is great, but fairly one dimensional - pan flat and on an old railway almost all the way. It's good fun if you want to just smash out 40 miles of actual gravel and rack up some miles.
Can't speak for the bit along the coast to Brighton, but I'm sure someone else can comment on that.
Is the Hot Chilee off-road London -> Brighton the best route? Anyone have any experience of it? Planning on doing it next Friday