You do need a licence for iplayer but only if you're streaming LIVE TV, not for recorded programmes. That said they are quite likely to come round to your house and harass the hell out of you because you've had a licence previously and no longer pay up.
I know this because I worked at a community centre as a volunteer which ditched the telly and was hounded by the licence enforcers because they were a soft target. Be firm, explain that you DON'T watch live TV and as they have to catch you doing it and the onus is on them to prove you ARE rather than you proving you're NOT, you should be OK.
Just don't expect them to live you alone for a while,