There is NO license fee for only using iPlayer
If you have BOTH an antenna and a TV Tuner capable of receiving broadcasts (eg. TV card, TV, Freeview box), you have to pay the license.
If you have only one of the two above things, you do not have to pay as you are technically incapable of receiving broadcasts. If you are capable of receiving them, whether or not you do, you have to pay.
And I'd gladly pay the licence fee for shows like QI, Top Gear and F1 coverage, Armstrong and Miller and so much more, all commercial free. Not to mention iPlayer. I can't handle american TV channels the few times I've tried watching it. Watching one show made me want to scream in frustration at the length, frequency and sheer 'annoyingness' of the ceaseless adverts. I can hardly watch ITV or Five at all either.