A regular respondent (Matthew) writes:

The program you are talking about was part of Nationwide, it was called
'Down and Out' and featured a journalist called Tony Wilkinson. If I
remember rightly, he was badly beaten up a few weeks after it was
screened, presumably by people who didn't like what he revealed. I
remember the program having a great impression on me; particularly the
part where he goes to stay in a grim hostel called 'The Spike' - having
had to spend most of his cash on burgers, because he had too much money
to get in). What's really scary, thinking about this now, is how much
worse homelessness has got since then.

I think he made another documentary where he pretended to be from
Scotland, coming to London in search of work (though I may be confusing
it with 'Down and Out').

There doesn't seem to be much on the web about it, all I could find were
a couple of oblique references:

http://tv.cream.org/arkn.htm

http://www.digitalgarage.co.uk/cv/biffincv.htm

I don't imagine Tony Wilkinson would fit with the BBC these days.