Looking for the King. David C. Downing

It is 1940, and American Tom McCord, a 23-year-old graduate student, is in England researching the historical evidence for the legendary King Arthur. There he meets perky and intuitive Laura Hartman, a fellow American staying with her aunt in Oxford, and the two of them team up for an even more ambitious and dangerous quest.
Aided by the Inklings – that illustrious circle of scholars and writers made famous by its two most prolific members, C.S. Lewis and J.R.R. Tolkien – Tom and Laura begin to suspect that the fabled Spear of Destiny, the lance that pierced the side of Christ on the Cross, is hidden somewhere in England.