- You may be looking for the in-universe division of the BBC.
CBeebies is the brand under which the BBC in the United Kingdom broadcast programmes aimed at children in the 3-6 age demographic. It was originally a subset of CBBC, before being given its own channel in 2002.
It broadcast Doctor Who: The Bedtime Story, a special episode of CBeebies Bedtime Stories, on 24 November 2023, in which David Tennant, in character as the Fourteenth Doctor, read aloud The Way Back Home by Oliver Jeffers.