On my daily route from my London home (in zone 3) to work (in zone 1) I will see about one or two Eastern European 'beggars' who I just walk past. No beggars at bus stops, very few if any outside tube stations, zero anywhere within the tube station itself, and maybe 1 or 2 on my walk to the office from the station. There are usually one or two I feel sorry for and maybe even contribute by buying them food or some change. At no point do I feel any of them might be a drugged crazy that will stab me for 20p. And I know for 90% of the people 'on the street' there is help even if it doesn't directly take them off the street at once.
If I saw any more homeless than that, and in worst state, i.e. children (no I don't mean the Eastern European ones wearing brand new Nike t-shirt trainers while their mums beg) then I would probably break down in tears. People in London just aren't used to seeing squalor that Europeans and Amercians have become accustomed to in their major cities. These are the unquantifiable differences between living in London and other major western cities.