Yes, looks like the spot just north of the East Heath Road car park. I vaguely recall it being cordoned off for a while, but assumed it must have been related to the Hampstead Heath Ponds Project or something like that. It's not unusual to see cordons around there. They even had the top of Parliament Hill fenced off a few weeks back for filming a scene in one of the new Marvel films. Just goes to show that there could be all sorts of things going on that locals don't know about.
That said, its hard not to notice the big increase in homeless there has been in London over the past 5-10 years. I don't think that is all due to rising house prices - there are other factors like the big sell off of social housing.
Anyway, the bunker sounds ingenious, but is nowhere as big as that of the Mole Man of Hackney[0].
[0] https://www.theguardian.com/society/2006/aug/08/communities....