Can I assume that all other apps can be updated and downloaded without issue? If so, try this.
Close the App Store app and the BBC News app completely and reboot the iPad.
Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the apps that you want to close, and then swipe "up" on the app preview thumbnail to close them.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.