From what I can remember you need to pick a terrestrial channel possibly none HD. Then go in to settings
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Then display & sound and click on screen.
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In this menu change the display area to +1 and the wide mode to full. Then launch iplayer and it should be zoomed out.
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Sadly I’ve only done this using terrestrial channels.
Also this initially messed up BBC HD into a stretched image, but putting the wide mode back to auto fixed this without altering iplayer. Makes me think you need to trick the tv into changing the aspect ratio of iplayer. Hopefully this will help.