Ah the family / mountain bike balance is always tricky
I'm lucky in that son is just about old enough to take with me
There was an online survey up during the summer, it was here ....
https://www.cityoflondon.gov.uk/things-to-do/green-spaces/epping-forest/about-us/Pages/consultations.aspx but is gone now that it's finished.
It was a survey about the usage of the forest, not just bikes but horses, walkers, parking etc. The survey results and the City of London's reaction to it haven't been published yet so not much to say or do about it until we know that there is a problem for us.
Within the survey they mentioned a few issues re erosion and damage to the local flora and fauna. Specific mention was made of jumps being built something they have, in common with most owners of public access land, problem with.
I got the feeling ( and from talking to the forest rangers in the past ) that they don't have much of an issue with the more natural trails. Where the problems seem to be is with stuff which is obviously built and where the impact of the riding effects large or specific areas.
It could be that they decide they don't have to do anything other than remove the jumps, built stuff as and when they find it. At the other extreme they could ban bikes from the forest and say just the fireroads......
Also worth mentioning that there seems to be a problem with night rides and there was specific mention of theses being banned.