Aha... so it's Projectivity is it? I'll try disabling and see if it'll then let me update iPlayer to the latest version (I couldn't find a way with it installed)
Ok, it's not Projectivity. It looks like iPlayer has been removed from the app store on that device, so it can't be updated to the fixed version. Boo.
Workaround!! If you have BBC Sounds installed, keep that, but uninstall iPlayer. Then, open BBC Sounds, and it'll say "can't find iPlayer, please install it" and that gives a direct link to install the latest iPlayer version. No idea why BBC iPlayer isn't showing up in search results on the Play Store though.