As long as you don't mind American voices, then you can find various stories on-line.
LightUpYourBrain - includes some Peter Rabbit stories.
Podcast of bedtime stories
StoryNory - The Ordinary Witch
Stories from the 60's
LibriVox - various public domain stories. Many are for adults, but you may find some suitable for children.
AudioBooksForFree - though only free at low bit rate, plus registration required. You can listen to samples though, before deciding to register.
Kids Audio Books
Lit2Go - not all children's books, but various titles.
Cbeebies Best Bits - Podcast
Cbeebies Radio - you can play the current show, plus selected stories using the Radio Player. You could record that output to a MP3 file, using something like Podcast of bedtime stories0
Podcast of bedtime stories1 - currently "Lea and the magic sunflower" is Free.
Podcast of bedtime stories2 - Podcast and Downloads
Podcast of bedtime stories3 - various stories in audio, not only children's titles.
Podcast of bedtime stories4 - various, some children's titles.