Ever since the Enlightenment a stream of critical scholarship has declared it impossible. It was often argued that the gospels reflected the needs of the early church, rather than the actual events which happened during Jesus' lifetime. Prof Richard Bauckam (whom I had the privilege of meeting last week!) offers a fresh and significant alternative to that status quo. In his groundbreaking book Jesus and the Eyewitnesses, which earned him the Michael Ramsey Prize in 2009, Bauckham makes a significant case for the reliability of the Gospel accounts of Jesus based on new research relating to among others the modern study of memory, especially in cognitive psychology. Check out the YouTube link:
Google books offer a relatively extensive exerpt from the book. It is free: