Undoubtedly, the crown owns any "unowned" land. In cases where there is disputed title, the courts are the arbiter. There are probably not too many disputed titles anymore since the introduction of land registry was in the 18th century.
Unowned land typically reverts to the occupier rather than The Crown. When I moved to London I used to live in Shoreditch, and there were many crumbling down buildings and second world war bomb sites, including one next to me that had been occupied by a rag-and-bone man for many years. When a developer wanted to buy the land for redevelopment, the original owner could not be found, and ownership was eventually reverted to the rag-and-bone man. There are many such stories of squatters inheriting valuable homes, e.g. https://en.wikipedia.org/wiki/Rainbow_George_Weiss .
Thank you. I am not British, and I had forgotten that particular fact. Technically, the concept of "adverse possession" exists in Canada, as well, but in practice it doesn't really come up (either eviction proceedings occur quite quickly or in the case of a small piece of land--a fence in the wrong place, perhaps--the owner may "give permission" which is enough to maintain ownership rights). I suspect that it does not come up often in the UK, either. Post-WW2 was a bit of a special case.
Anyway, the land in your example was not really "unowned." Rather the legal owner was different than the occupier, and turned out to be missing. I was referring more to the fact that the Crown is the ultimate legal owner of (essentially) all of the land in the UK (and Canada and other countries for that matter). Anything that does not have any other legal owner is definitely owned by the Crown. What would be called government land in the US is called Crown land in Canada (and presumably in the UK?).