But then surely the West Anglia lines are a bit different, they're mainly commuter lines, rather than previously underused radial routes. I doubt there's much latent demand there, such that numbers will now rocket under TfL (as opposed to steadily increasing like the other commuter routes)
I would disagree with this slightly. The corridor from Stoke Newington to Edmonton Green is tremendously busy - it has an extremely frequent parallel bus service. For longer trips then trains will be far faster if your waiting time is low. I expect that there has been and will continue to be some modal transfer from bus to rail once people realise there is a rail line there - the famous "tube map" effect. The problem TfL have is that they can't hugely increase train frequencies and thus lower wait times. If they could do this then the modal transfer would, IMO, be rather higher.
The fact that stations are staffed and have been improved has also changed things. From my occasional observations places like Bethnal Green are vastly busier now than they used to be 10, 15 or 20 years ago. I haven't noticed massive changes on the Chingford line but I expect it is busier off peak. It was always and remains busy in the peaks as is the route via Seven Sisters.
The patronage stats, in the London Datastore, for London Overground show continued growth but unfortunately the numbers are not broken down by line / route.