Even quicker guide to listening to BBC Radio 1 on your iPhone:
Hijack BBC headquarters and eradicate the useless format!!!
lol.. or I guess convince Apple and Tuner to use Real Media and Windows Media!!!!
For Windows users the equivalent to Nicecast would be Shoutcast for Winamp.
I listen to a lot of BBC 1, specifically the 1xtra programming, so I'd really love there to be a feasible way of doing this. But running your own stream to broadcast would use a lot of home bandwidth if you were to leave it frequently while you're out.. which you would have to do to make this worthwhile.
Great tip though!