If no one can afford to pay it what is the government going to do? Raze the buildings?
In the UK, there are two kinds of ownership for a property: Freehold and Leasehold. Freehold is simple, you own the land and the building. Leasehold is usually for flats/apartments but can sometimes be for other types of property. A leaseholder owns a lease entitling them to live in the property for X number of years (100 years is common, but 1000 years crops up sometimes). So you can own a 100 year lease, live there 10 years and sell a lease with 90 years left to run when you move out. But there are certain obligations to a leasehold, like paying a fee to the freeholder for maintenance on the building. I think if you continually fail to pay the maintenance fee you would eventually lose your lease, which would allow the freeholder to sell a new lease on that flat.
So if the residents can't pay, they will eventually be forced out of the tower block, the freeholder can do the work and sell the leases again for £300,000 a pop. That figure being the estimated value of the flats stated in the article.
As the property is privately owned, it looks like there is nothing the government can do about it - other than offer to cover the costs, which they wont do.