It turned out that much of this was actually on the London Loop. Again.
My plan had been to walk around King George's Reservoir until I ran out of footpath. The walk along the reservoir was quite pleasant; there were trees and swans and amusing signs. However, when I rounded the top and prepared to walk back down the eastern edge, I found that the footpath that was clearly marked on my A-Z was blocked off with hazard tape. However! There was a very clear gravel path leading off vaguely northeastwards, and a sign proclaiming it to be the way to Chingford Station — three miles, which sounded about right. It all got rather organised-looking at this point; not just the nice gravel path, but benches every fifty yards and even picnic tables. This, it seems, was the bottom edge of Lea Valley Park.
About 500 m later, I reached Sewardstone Road. This was the part I hadn't been looking forward to, since it was basically a long trek down a main-ish road, and Google's satellite images had suggested that there wasn't much pavement involved. (My previous footpath plans would have had me coming out onto this road about a kilometre further south than I actually did.) I was momentarily cheered by seeing a sign for "Freddie's Free House", but it turned out that this was in fact an ex-pub, not a pub. I did see a foreign bus, though, and what seemed to be some kind of llama petting zoo. And of course ended up in a pub.
Next up: I've actually finished the top row now, but I'm going to try to keep a continuous line, so I'm walking off-map from Chingford Station around to Chigwell Station. I had to purchase an extra map (from Stanfords) — it was very exciting.