Apparently a new book is out (or perhaps is about to come out), analyzing Doctor Who and race, and it has angered someone at the BBC enough that they've come out with a response to the charge that the show is "thunderously racist". The article gives no further information about the book, but a quick Google search turns up this site that seems to be intended to promote the book. This seems to be the call for papers, giving a sense of what the publisher or editor wanted the articles to be like before any of them were written.
I have two thoughts. One is that the pushback from the scifi blogs and from the BBC, pointing out ways Doctor Who is racially forward, seem to me to be generally accurate. Consider the contemporary show especially. Martha Jones was by far the most intelligent of all the recent companions, and she's black. She was a medical student, even, and she eventually became a doctor. The other recent companions have mostly been working-class women with much less education. They dealt with the inter-racial relationship of Mickey and Rose as if that were perfectly normal. There have been plenty of guest starts, and those of non-white races have not seemed to me to be remotely racially stereotypical in most cases.
There might be racially insensitive moments of the original series, reflecting those times (meaning that it's not any more racially-insensitive than anything else in those days). The show started in the 1960s, after all. There were several early serials where the reality of the available actors in the UK at the time required that they use white actors to play Aztecs or the soldiers of Genghis Khan. If you did something like that now, you'd better do it right.
Some say the SNL portrayal of President Obama by a white actor was much more successful at this than most instances of blackface. It remains to be seen whether Johnny Depp will get away with his Tonto in the Lone Ranger later this year. But in the 1960s, when the actors you had available were all or mostly white, you had to make do with what you have, and the issue is mainly not who's playing the characters but whether they act in a way that furthers harmful stereotypes. In my judgment, most such instances on Doctor Who do not, at least where I am in the series now, which is 1971, with a smattering of episodes throughout the later Doctors and then the new series through the early sixth season.
As for the claim that primitive cultures are portrayed as savages, all you need to do is look to the second serial, The Daleks, where the Thals, who had gone primitive after centuries of post-apocalyptic avoidance of technology, were anything but savage. It was The Doctor who convinced them to overcome their pacifism and fight back against the Daleks. There was even the serial called The Savages, where the idea that they were savages was held by the dominant technological society in that world but turned out to be false, and at the end they have to learn to live together in harmony. And those examples were both in the 60s.
The reality is that a long-running show like Doctor Who will eventually display the prejudices of its times, but it has many, many moments of breaking away from those, and it often has done so in creative and helpful ways, using alien races as analogies for human racial relations or for colonial or slave relations. It's perfectly legitimate to point out ways Doctor Who has assumed cultural superiority of certain groups and such, assuming it has done so in the particular cases. It's fine to point out ways the show has represented stereotypes when it has done so. But it does not do to make blanket statements based on a few individual cases about the show as a whole, especially if the current show is implicated in problems with past representations. And if you talk about Doctor Who now, it doesn't make any sense just to point to examples from decades ago.
So that's my first thought. The reaction of Doctor Who fans and the BBC to the charge of racism seems to me to be largely correct. The show doesn't seem to deserve the label "thunderously racist". The criticism seems to me to be ill-informed.
But that brings me to my second thought, which is that the knee-jerk reaction doesn't strike me as very informed either. Take a look at the call for papers, and then go to the site promoting this new book to see what the various articles in the book are actually doing. Here is a list of the main points for each chapter