Since your audio stream is (presumably) being played through the Safari browser, it will still play because of multi-tasking which allows it to run in the background. You need to double-tap the
Home button which will bring up the multi-tasking bar at the bottom of the screen.
If you have several apps open, you may need to swipe across the screen until you come across the Safari app. Now press on the app until it starts to wiggle and you will see the red minus sign on the app. Tap the minus sign and that will close the app once and for all.
When you are done, tap the
Home Button one time or anywhere on the main screen above the bar to stop the wiggling and close the multi-tasking bar.
Clear as mud, eh?