I read the The Horse, the Wheel and Language recently and was bedeviled by the discrepancy between the BP and BCE dates given. BCE dates are Before the Common Era, meaning dates relative to the our current calendar and generally derived from non-carbon-dating methods. BP is Before Present and means years before 1950. BP dates are carbon dated. The 1950 reference is because that was when the carbon isotope distribution began to change because of nuclear testing.
The problem is that when the author gave both BCE and BP dates for an event, subtracting 1950 from the BP date did not give the BCE equivalent. There are some known sources of error in carbon dating, but these did not seem to be nearly enough to explain the large differences in the dates.
What explains this discrepanacy?
He explains in his appendix (p. 467) that when he quotes BP dates, he's quoting uncalibrated dates, that is to say, raw radiocarbon "age". This isn't at all the same thing as a calendar date, and needs to be converted to calendar years by means of a lot of dendrochronological data.
The upshot is that uncalibrated dates are significantly "younger" than actual calendar dates, and the discrepancy between calendar date and uncalibrated date increases the further back you go.
It isn't standard to quote uncalibrated dates as "BP". But then again it's not a technical publication, he does explain it, and he does it consistently (at least, one hopes so: I'm not going to check every date in the book).
(Incidentally, to convert BP to BCE, subtract 1949, not 1950. That doesn't account for the discrepancies you've noticed of course.)