Here are the official British Broadcasting Corporation directions for knitting a "Dr. Who" scarf:

Materials: Size 4 (American size 10) knitting needles; 26 25-gram balls of double knitting (American worsted weight) wool in the following colors: 3 purple, 6 camel, 3 bronze, 3 mustard, 4 rust 3 gray and 4 greenish brown

Directions: Using purple yarn, cast on 60 stitches. In plain knitting (garter stitch), always slip the first stitch in each row. Knit rows in the following order: 8 purple, 52 camel, 16 bronze, 10 mustard, 22 rust, 8 purple, 20 greenish brown, 8 mustard, 28 camel, 14 rust, 8 bronze, 10 purple, 42 green, 8 mustard, 16 gray, 8 rust, 54 camel, 10 purple, 12 green, 8 mustard, 18 rust, 8 purple, 38 bronze, 10 camel, 8 gray, 40 rust ,14 mustard, 20 green, 8 purple, 42 camel, 12 bronze, 20 gray, 8 rust, 12 purple, 6 camel, 54 green, 16 rust, 12 gray, 8 mustard, 20 bronze, 10 purple, 12 camel, 32 gray, 10 rust, and 16 mustard.
The tassels at each end of the scarf are made of 1-foot lengths of wool, using all seven colors.

The BBC, which licenses all "Dr. Who" merchandise, warns that the finished scarf is to be worn, not sold.

Paula's notes: I sent for this pattern back around 1980. I think TV Guide offered it. DK weight yarn was rare enough in the US that I'd never heard of it. I'm surprised that they suggested worsted weight as a substitute. If I knew then what I do now, I would've gone with sport weight. This scarf in worsted weight is HEAVY, though I don't imagine it is exactly light in double knitting. For authenticity as well as comfort, I'd do it in DK with US size 6 needles. A much later note: These may well be the official BBC directions, but they are not accurate.