Yes, the number of homeless people is increasing year on year. A major contributor to this problem is that there are simply not enough affordable homes, either on the market or being built. There are two sides to this coin though, one side is not enough housing available for the people looking for somewhere to live, the other side is more people looking for housing than the housing market can supply.

One side can be addressed by an increase in house building, the problem from the other side is more difficult to resolve, that Grauniad piece of BT's above is from 2013, in the four years since then the population of the UK has increased by 2 million, almost entirely due to immigration, and these people need somewhere to live. The miracle is that the number of homeless people isn't rising much more with such a huge population growth year on year.

But this is the elephant in the room, no one wants to talk about it, an increase in homelessness is an inevitable consequence of open borders, free movement of people within the EU. But anyone suggesting that we try to regain control of our borders and attempt to reduce the increase in population growth is howled down as a racist bigot, and all the while the number of homeless grows and we expect our tiny overcrowded island to accomodate an additional half a million people year on year. Can't be done.