I did something close to this route last year with a few friends. We immediately decided not to follow the UK side of things, it's utter nonsense. We followed something like the L2B route which is a pleasant ride. The Newhaven-Dieppe ferry is good 'cos you can get a cabin on the overnight ferry.
The french side was a dream, the avenue vert currently starts near dieppe and follows an old rail line for 30k. No traffic, wide and smooth, and the pedestrians moved out of the way of us and waved. After the railway ends it was back on the roads which were a delight, the only other off-road section was the forests outside Versailles. I'm not sure that are planning to make the whole route a cycle-lane only affair and if they do it will be a real shame.
One night on the ferry (£20ish), one night in a farm house (with breakfast in bed - £15), one night in Paris (£50) and a one way on the eurostar (£40). Worth every penny.
Hint: Clear your cookies and tell the eurostar site that you are Australian - It will let you buy single tickets at a much more reasonable price.