""Why should he not want to come here and live in safety compared to what he may have left behind?""
The issue is, that no-one knows this mans history. He might be in the country, legitimately, if he is, then he will get his basic needs provided for. If he isn't, then someone, somewhere should know about him.
This might sound harsh, but begging shouldn't and can't be a persons only means to income.
"No-one begs for fun""
No, they beg for money and depending on your background etc, that dictates how you feel about it. Some people have been sent out begging, as children, in their birth country. We need to work with those people to give them a chance to make their own choices and make a better life.
Recently in Morrocco, we were told not to buy tea or give to the children, because no-one, in the area (not speaking for the entire country) were poor enough to not send their children to the charity provided school. They'd send their DD's out from about 8 years of age, often with younger ones, to earn money.
When we take accept Asylum seekers and Refugees, we shouldn't do so and leave them to a life of begging. It's a culture that we can't allow to continue in the UK. We have a safety net, we need to teach them that. They don't have to accumulate and put away money for when they are sick etc. That's a real fear, for some people, that needs a good funding base to help them recover, psychologically.
I mentioned in my earlier post about well published phone numbers, there should be a service for those holding signs, as in the OP, before we have to involve the Police.