I think the difference is that the US has abject poverty at levels that call into question its status as a proper first world country. So many of these people probably simply require some basic mental health/rehab services, but they just have too many hoops to jump through to get them (assuming they qualify for Medicaid or other assistance, which isn't necessarily a given). It's not surprising that a country like Britain with reasonably accessible social services has way fewer people in this condition. To your question about why they've taken over public transit in particular - I think the situation is just that out of hand. Libraries and parks are similarly full of homeless people, probably just due to the fact that they're public.