The BBC found the head of a policy institute to criticise the figures, and, judging by a comment by one of their correspondents in the studio afterwards, that institute is a staunch supporter of George Bush (who also disputes the figures). This makes it clear that you should always ask who has produced the publication or website that you are looking at.
They also stated that the publisher supported the research, and backed this up by producing the editor of the Lancet (who wrote an article in the Guardian on the 12th).
The Guardian headlines the story "One in 40 Iraqis "killed since invasion"". Not sure where that quote comes from, but I want to read the paper to see if that is really what it is saying. 1 in 40 may well be so, but I thought the paper was talking about excess deaths from all causes, not just people killed. (Reading the paper: most of the deaths are attributable to violence).
The paper has now appeared in the Lancet, as Lancet 2006; 368: 1421–28. You can also find it by going to http://dx.doi.org and pasting this DOI:
into the search box.
Science (20th October 2006, p.396) reports a debate that has now started over the methods of this paper, and whether the sampling method and extrapolation is valid. The Guardian, certainly, has picked up on this debate as well.
The Lancet of 13-19 January 2007 includes several letters in response to the original article.