I just happened to see this now. DannR, I don't think you read the question correctly.. The OP does NOT want the phone to record the external sounds. He/She just wants to record the incoming audio from the Net.
Siberian, do you want or need to listen to the stream as it's coming in? If not, you can buy a plug with nothing on the other side, This should eliminate your external noise problem. If you do want or need to listen while you're recording, you can get some headphones to listen, but if they are connected to that plug, you might still get the ambient noisae. Speakers can be used as microphones too. I don't know if using Bluetooth will still allow the ambient noise to be picked up. You could try and experiment.