Homeless people with dogs

So I know this will probably yet a lot of mixed views and that's okay.

A while ago I was watching videos on YouTube of people helping homeless people. I came across a video of someone who had witnessed a homeless mans dog being taken away from him (by someone who had the authority to do so).

The homeless man was obviously heartbroken as the dog was the only thing he had left that brought joy into his life.

What are your opinions on this? Do you think that homeless people should be allowed to keep their dogs? I have mixed thoughts as I live in England, and in the Winter our weather can get extremely cold with very heavy rain. I don't think the dog should have to suffer because their owner is on the streets, but I also think they should've helped the man out too.