You are in luck if you want traffic free, because you can do virtually the whole journey traffic free.
From Kings Cross you need to get to Angel, from where you can pick up the Regents Canal path. With a left at the canal running alongside Valentines Park, you can pick up the River Lea route near to the Olympic Stadium. Heading north the path is mostly paved until you get to the A406, when it becomes a gravel path. Keep heading north, and watch out for the bridge that takes you onto the River Stort path.
The River Stort path is more like a footpath in parts than a cycle path, but it is a cycle way. At Bishop's Stortford, you'd need a road route for a couple of miles to the other side of the M11, from where you can pick up the Flitch Way. The Flitch Way is a shared use path that follows the old railway line from Bishop's Stortford to Braintree.
So apart from the initial bit from Kings Cross to Angel, and the bit in Bishop's Stortford from the town centre to the M11, you have an off-road route for the whole journey. I've ridden all the sections of this route multiple times.