Is television the enemy of books, or their friend? Literature has certainly been a healthy source of inspiration for television drama, and continues to be, but in recent years the coverage of books on TV has been missing or execrable. Radio 4 remains serious about books, but on television they are sidelined to the edges of BBC2 or BBC4 (and the axing of Newsnight Review didn't help either).

But could all that be about to change? This week the BBC has announced a new series of programmes about books centred on marking the 400th anniversary of the death of William Shakespeare. Jonty Claypole, the director of BBC Arts, says authors have books have always been at the heart of the BBC and the new programmes are about pushing them higher up the agenda. In reality, it feels like making up for lost time.

The new season does offer some promising programmes though and among the most promising is a new BBC 2 documentary about Roald Dahl. Not only does it involve his long-time collaborator, the illustrator Quentin Blake, it draws on letters and diaries to explore where the creative madness came from. There is also plenty of archive interviews with Dahl, shrivelled and inventive, like the third Brothers Grimm.

There are also several programmes celebrating the Brontes, among them Living Like a Bronte in which Martha Kearney and the novelist Helen Oyeyemi travel to Haworth Parsonage, the home of the Bronte sisters, to discover the stories behind their classic novels. On BBC4, Brontes at the BBC also uses the archives to discover more about the lives of the sisters.

The programmes on Shakespeare will start on April 23, the day of his death, and continue for a month across television and radio. One of the highlights will be Russell T Davies' version of A Midsummer Night's Dream. He has always been slightly obsessed with the story and has been filming it in Cardiff (where he used to make Doctor Who) over the last few months and the cast is impressive and experimental: there's Maxine Peake, Richard Wilson and Elaine Paige among others.

BBC 2 will also be showing the next instalments of The Hollow Crown, the BBC's adaptations of the history plays. Tom Hiddleston was extraordinary in Henry IV, parts one and two, three years ago and the season will continue next summer with Henry VI and Richard III. The cast reaches the same heights, with Judi Dench the best of them.

The aim of the Shakespeare season, according to its makers, is to get more people enjoying Shakespeare by putting it at the heart of the schedules, but there is also a more direct attempt to get young people distracted by their tablets to read as well.

The new BBC 4 documentary B is For Book will follow a group of primary schoolchildren as they learn to read, but The Book That Inspired Me goes into schools and tries to encourage children to read specific books. They also discuss what has been holding them back from picking up a book.

Part of the explanation in recent years is the BBC itself, which says it puts books at the heart of the schedules but doesn't really. The One Show has a regular feature called Britain by the Book, but most of the BBC's coverage of books is limited to late night on the secondary channels. Imagine, for instance, has done some good documentaries recently on Colm Toibin among others but later-night BBC2 shows do not make up for the lack of coverage on the other channels at times when young people might be watching.

The new season of programmes is at least a start, or the beginnings of a recovery. The director general Tony Hall says he wants to ignite a spark in people. "Let's not forget, a book can change your ideas," he says. "It can change your life." The hope is that the BBC is now beginning to do more to make that happen.