There is an obvious way that Doctor Who could be related to the Jesus tradition: we just need someone with a TARDIS to go back and record what Jesus said and did, which we can then compare with the later Gospels.
Since that is not currently feasible, here’s plan B (which Judy Redman began to elaborate on her blog, based on a comment I left there). We can take a television show (LOST would work, too) and get people who are enormous fans to agree to watch an episode only once and then try to recall exactly what the Doctor said and did. If we get people who have never watched the show before, people who like it and people who love it to all do this, we can also see how the importance of the Doctor’s words and actions to an individual influence the accuracy of preservation.
The reason for doing this is not simply a desire to find a way to bring together Doctor Who and Biblical studies together for the sake of those who love both. There are few similar situations to that which would have existed in early Christianity, in which Jesus had disciples/students who would have made an effort to preserve his teaching, but would not have had the benefit of written notes in most if not all cases. And so checking the recall of the Doctor’s words and actions on Doctor Who (or the words of Jacob or another main character on LOST) might be the closest parallel we can study in our time.
Of course, Mark Goodacre will probably point out that unless the episode of Doctor Who they watch is voiced over in Koine and the viewers understand it fluently, then the situation will not provide a precise parallel or render accurate data on the number of words that can be recalled verbatim without the assistance of a text.