I did that route over a couple of very hot days this summer. 10 hours-ish sounds about right. Just looked at my strava and I was moving for approx 12 hours. But assume you'll be faster than me, even at relaxed pace.
Speed is very uneven though - the Downs link bit is almost all flat gravel paths and is really quick (though not hugely exciting). But then some of the South Downs sections are pretty slow going.
If it's muddy I'd allow considerably more time for all the offroad bits. Plus extra time for mechanicals, etc.
If you've got 2 whole days to do it then it will be very relaxed - I didn't leave London until after lunch on the first day and had assumed I'd be easily back to collect kids from school on second day, but ended up taking much longer.