I cannot find BBC iplayer on my Roku express. It was purchased in the UK.

Do you see other apps that are only available in the UK like ITVX and Channel 4?  I don't know if it's BBC iPlayer, but I believe there are apps that are only available on certain devices.  If you don't see ITVX and other UK apps when you search for them in the Streaming Store, there may be a problem with the region associated with your Roku account.