Almost three in 10 children do not know that the Nativity story comes from the Bible, while many others do not identify Adam and Eve or Noah's Ark as religious tales, according to new research.
It reveals that while many parents think it is important that their youngsters are aware of the contents of the Bible, high numbers of boys and girls have never heard, read or seen some of its most famous stories.
Bible Society, which published the research, said the findings suggested that Bible literacy was falling, and that while many people still placed great importance on the book, little was being done to ensure that more people engaged with it.
The report, based on surveys of around 800 eight to 15-year-olds and about 1,100 parents, found that 29% of children did not think that the Nativity came from the Bible.
One in five (20%) did not pick Noah's Ark as a Bible story and a similar proportion (19%) did not choose Adam and Eve.
More than a third of the youngsters questioned (36%) did not select the Good Samaritan as coming from the Bible, while two in five (41%) did not identify David and Goliath as a religious story.
But almost one in 10 (9%) wrongly thought that the stories of King Midas and Icarus were from the Bible, while 6% thought that the tale of Hercules was contained in the book.
The Society's report said the statistics were "symptomatic of the fact that many children indicate they have never read, seen or even heard these stories".
Nearly a quarter of children (23%) had never read, seen or heard Noah's Ark, along with 25% for the Nativity, 38% for Adam and Eve and 43% for the Crucifixion.
The study went on to say that it was not just young children who were unaware of classic Bible stories, with older children perhaps faring worse, "possibly as their engagement wanes and memories falter".
In total, 30% of secondary school pupils - aged 12 to 15 - did not pick the Nativity as a Bible story, it found.
The report also warned that Bible literacy was little better among adults, with some finding it hard to distinguish between the plot lines of well known Bible tales and famous films.
Nearly half of the parents questioned (46%) failed to identify the plot of Noah's Ark as a Bible story, while around a third were unsure or did not recognise the tales of David and Goliath (31%) and Adam and Eve (30%) as being from the Bible.
But more than a third (34%) thought a Harry Potter plot line was from or might come from the Bible, while over half (54%) said the same about a plot line belonging to the Hunger Games.
The report found that almost half (43%) of parents whose children had seen, heard or read Bible stories said it was important for a child to do so because these tales provided good values, while two in five (40%) thought these stories were important to our history and culture.
Three in 10 (30%) said it was important to ensure that classic stories and books were passed on to future generations.
It also revealed that over a quarter of children (28%) said they would like to read, hear or see more Bible stories.
The Society published the research to mark the launch of its new Pass It On campaign, which aims to encourage parents to keep the Bible alive by passing on its stories to their children.
In a foreword to the report, Dr Richard Chartres, the Bishop of London, said that sharing Bible stories "is as vital now as it has ever been".
"Too few children have the opportunity to hear and reflect on what this life-changing book contains," he wrote.
"Even those that do when they are young often take its awesome stories for granted when they become adults.
"There is work to be done."
James Catford, group chief executive of Bible Society, said: "It's clear that parents want to give their children the best start in life.
"The Bible's contribution to our culture - language, literature, the visual arts and music - is immense.
"It doesn't matter who you are or where you come from.
"The Bible enriches life, and every child should have the opportunity to experience it.
"If we don't use the Bible, we risk losing it.
"We're calling on parents to pass it on."