Is there proof that "a high proportion of homelessness is caused by substance abuse ..."? By proof, I mean reliable, reputable studies that show this.
The fact that many rough sleepers abuse drugs and/or alcohol doesn't automatically mean that their substance abuse predates their homelessness.
If I were to find myself in their predicament, living rough, with no family or friends to turn to, I am quite certain that I too would start to abuse alcohol to dull the (mental) pain and the cold, but it certainly wouldn't be the cause of my plight!
To be honest, when I imagine myself in these people's shoes, I find it hard to see a way back for them, even for those not taking drugs or drinking excessively. How can you possibly turn your life around when you have absolutely nothing, and nowhere to call home? It doesn't bear thinking about!