My take on this is as follows (I'm in the uk btw):
There is no BBC iPlayer app, just got to www.bbc.co.uk/iplayer in safari and you're away
As for Uk iTunes account, I'd guess it's a similar approach we Brits use to gain access to the US store - ie sign out of the app store/iTunes store, download a free app and then you will be asked to sign in or create a new account. Just create a new account but make sure you change the country before doing so to create a UK account. All sorted. If you want to download payed for apps you will need to pop into a store (apple, supermarket, or many others) and just purchase an iTunes gift card.
You are better off using your US iTunes account while in the UK, there no advantage using a UK iTunes account at the moment. I'm in the UK and use a US account all the time.