Re: Uh... NO!
You do not need a TV license to watch catch up programmes on the BBC I-player. From the BBC website:
"You do not need a television licence to catch-up on television programmes in BBC iPlayer, only when you watch or record at the same time (or virtually the same time) as it is being broadcast or otherwise distributed to the public. In BBC iPlayer, this is through the Watch Live simulcast option.
Anyone in the UK watching or recording television as it's being broadcast or simulcast on any device - including mobiles, laptops and PCs - must, by law, be covered by a valid TV licence."
So no live Olympics without a TV license but you can still get all the Doctor Who once it's up.