It seems that the BBC no longer supports the iPlayer service on Sony EX72_ models:
http://sony-eur-eu-en-web--eur.custhelp.com/app/answers/detail/a_id/141250
You don't need to buy a new telly though; you can simply buy an external device instead. For example, a Now TV box costs around 15 quid and includes catch-up apps, such as BBC iPlayer, as well as apps for watching things like Youtube videos on your telly. (Sky, who make the boxes, would love you to subscribe to their Entertainment, Film or Sports packages but you don't have to; the catchup apps, etc, all work ithout a subscription).