The campaign, created by Kitcatt Nohr Alexander Shaw, aims to encourage "hard to reach" parents to discover the enjoyment of sharing books with their children.
It features two 40-second ads called 'Pirates' and 'Space', which will run across 10 regional radio stations in the London, North West and Midlands areas, including Total Choice, Sunrise, Kiss 100 FM, Leicester Sound FM, Trent FM, Galaxy Manchester and Club Asia.
Both radio ads feature voice-overs from actor Tim Bentinck, famed for his role as David Archer in Radio 4's drama 'The Archers'.
One ad sets the scene for a dramatic pirate tale and the other, a story of space travel.
The strapline for the campaign is: "No matter when, no matter where, you can always take your children somewhere amazing. Take them into a story with Bookstart."
Listeners are encouraged to respond to the radio ads by texting 80800 free from their mobile phones to receive a fulfilment mail pack containing a free pirate-themed storybook and information about where to collect other free books.
Emily Butt, Booktrust marketing manager, said: "Kitcatt Nohr's intriguing radio ads encourage people to create imaginary pictures in their heads as the story unfolds and this neatly reflects the way we use our imaginations when reading a book.
"This campaign aims to reach people in society who don't think of book sharing with children as a matter of course.
"We hope these ads will prompt parents to text us to receive a free book to read to their children."
The radio campaign, which starts this month, follows two TV campaigns earlier this year.
Paul Kitcatt, creative partner at integrated agency, Kitcatt Nohr, said: "The ads make clever use of sound and dialogue to conjure up imaginary children's stories about pirates or travelling into space.
"The aim of the campaign is to remind the audience of how a good story can transport a child's imagination to myriad magical places without moving an inch.
"Our aim was to make the ads as fun and accessible as possible while highlighting the many benefits of reading to kids."
Media planning agency Trinity Communications carried out the campaign media planning.
Simon Timlett, partner at Trinity Communications, said: "We used geo-demographic tools to help us understand the best regions to reach this 'hard to reach' target group and as a result chose regional radio as the best media to engage this audience at reasonably low spend.
"We chose to repeat the use of a free text response mechanism due to the success of two previous TV campaigns this year which generated over 115,000 responses and because the audience has limited online access but high mobile telephone ownership."