Specifically, you can use all their services including the iPlayer as long as you don't use the iPlayer to watch a program as it's being broadcast.
http://www.bbc.co.uk/blogs/bbcinternet/2008/01/iplayer_does_...
I don't have a TV and I live in the UK and the licensing people are aware of this. I do have broadband at home. At first I thought I would watch TV via the iPlayer, but it turns out that I've watched a grand total of one program in the last four months.