According to a speech from Tim Davies, the BBC won't close BBC Four, CBBC and Radio 4 Extra for at least the next 3 years.
"Over time we expect to consolidate and share more content between services, and expect to stop broadcasting some of our smaller channels on linear. This will include services like BBC Four, CBBC and Radio 4 Extra. But we won’t do this for at least the next three years because for the moment they are still delivering value to millions of viewers and listeners, at low extra cost."
Tim Davies
"Over time we expect to consolidate and share more content between services, and expect to stop broadcasting some of our smaller channels on linear. This will include services like BBC Four, CBBC and Radio 4 Extra. But we won’t do this for at least the next three years because for the moment they are still delivering value to millions of viewers and listeners, at low extra cost."
Tim Davies