Nope, you don't actually have to make any purchase. I only had one to purchase US TV shows as they aired in the States.
If you go to the US store, and click the button to download a free app - it will let you create an account without having to add in a credit card. Sign up as normal, but put in a US address (I usually just use a hotels address).
Once that's done, just sign in to the US store on your phone and iTunes Radio should be available! Then, you can sign out and sign into your UK account to make any purchases.