Noddy

Noddy was a character from Enid Blyton's books.

When the Tenth Doctor was nonplussed at the extraordinary coincidence that Agatha Christie could be in the middle of a murder mystery or the idea of Charles Dickens seeing Christmas ghosts, Donna suggested the absurdity of meeting Blyton and finding her having tea with Noddy. She asked him if Noddy actually existed and he assured her that he didn't. (TV: The Unicorn and the Wasp)

However, one of the artefacts on the Dr Smith shelf in P.R.O.B.E. HQ, given to P.R.O.B.E. by various time travellers and left there until their purpose became apparent, was a complete set of Noddy books complete with a post-it note marking them out as "very important". (PROSE: Out of the Box)

Behind the scenes
Earlier in the same scene of The Unicorn and the Wasp that includes a discussion of Noddy, the Tenth Doctor refers to PC Plod, an insult referencing a character from the Noddy series of books.

On screen, Noddy has been voiced most prolifically by Susan Sheridan, who played the character throughout the entire run of (1992-2000).

In 2009, the blog Teatime Brutality jokingly asserted that, based on the Tenth Doctor's lines about Noddy in The Unicorn and the Wasp, Enid Blyton's Noddy books were the only work of fiction which could resolutely be stated to be non-canonical relative to Doctor Who, complete with a tongue-in-cheek "diagram" to this effect. This claim was later echoed in Elizabeth Sandifer's TARDIS Eruditorum.

References in invalid sources
When the First Doctor exhibited a great distaste for the BBC's New Adventures of Noddy, Susan thought he was exaggerating. Noddy then quipped that "They'll be taking Dick out of the Famous Five Next!" (NOTVALID: Doctor Who? 190)