It's an old law to dissuade vacant properties effectively, but people don't often use it within fair use, resulting in situations like this. It'll need to go to court, and they'll be evicted, but they'll claim it under squatters right (wrongfully.
This is an old practice in the UK, older than the US by many centuries, and it's why many states in the US also adopted it in some measure when the union was formed. Most countries have similar laws, and people are often surprised by that fact. Squatters were a common sight across the UK because no one effectively owned land - the monarchy or the church owned it. Traditionally in an English village, there were several classes of people. At the lower end were the incomers known as borderers or squatters, who would erect a cottage or a hovel on common or waste ground to house themselves and would pay rent to the Manorial lord or would work on his demesne several days a week. The building of the cottage was generally tolerated or even sanctioned under customary rights.
To understand the spirit of the law, I recommend reading about the 17th-century Diggers: https://en.wikipedia.org/wiki/Diggers
Your personal property is protected. Reframe the intent. Imagine if Blackrock or Vanguard came in and bought out a county, land property and all, then just left it completely unused and untended. The place would fall to squalor. Squatters' rights mean you could continue to live and work that land without their permission. It was common in the 60s and 70s for communes to move into unoccupied mansions in London (https://en.wikipedia.org/wiki/Squatting_in_England_and_Wales). Many of these homes were (still are) owned by oligarchs who had no intention of living there. They own it because it's an appreciating asset that drives up house prices in the area, forcing out local families, buying up the subsequent properties, and making ghost towns. Without a vacancy tax, there's no disincentive for people to own empty houses in places where people want to live besides the squatting laws.
It should be noted, that squatting in residential property became a criminal offence in 2012. "Professional" squatting happens now in vacant commercial buildings (like Ramsay's restaurant), or on disused land. The restaurant they're occupying has been vacant since 2015 - 9 years now. Squatters can apply to become the registered owners of a property if they have occupied it continuously for 10 years, acted as owners for the whole of that time and had not previously been permitted to live there by the owner. I guess these people will suggest that they have lived there continuously for the last 9 years (they likely haven't, which is why it'll get thrown out in court) and live there for the next year to try and take ownership.
They have a couple of Instagram accounts up about the whole thing it looks like: https://www.instagram.com/camdenartcafe/ https://www.instagram.com/autonomouswintershelter/