There's a useful discussion here about the pros and cons of the UK TV License. It actually starts off as an experience of the hounding that many people get who either do not want TV or find themselves an error in the licensing database. But it also includes some commentary on whether or not a license fee is the right way to go.
While in Canada I had an interesting experience watching US PBS one evening. This channel is available in Calgary and the local station in Spokane Washington (across the border) actually gets a lot of its funding from Canadians during pledge drives. Two hours of excellent TV started with a documentary (Nova) on the science behind Hurricane Katrina. This was followed by a fine piece of investigative journalism (Nightline) on what went wrong with the emergency response to Katrina. I felt very comfortable knowing that, because much of PBS funding is from "viewers like you", there is a strong disconnect between government and public media. As a result, the hard hitting piece was extremely scathing when it came to FEMA and "White House jobs for the boys".
While there is no doubt that the BBC could do a similar piece in the UK (about a disaster in the UK and its government's response) I feel that the public's reaction tends to be split on anything the BBC does. One of the favorite reactions always seems to be "this is not what I pay my license for!" The difference is, of course, that in the States you don't have to support public TV whereas in the UK it seems you do because the TV license is mandatory.
Would British viewers pay for PBS style programming if there was no license fee? Personally I doubt it. Not even enough to pay for the excellent radio services.