Of course such lists are inherently silly, and Wagner (to do her credit) more or less admits as much. Still...
According to Wagner: "we considered a number of factors — sheer quality of writing, longevity, lasting impact and, naturally, commercial success." Presumably JKR got in on the strength of the last of these, primarily - but if her, why not Barbara Cartland? As for the other criteria, I'm not sure what the difference is between longevity and lasting impact, but both would seem to discriminate against newer writers, in theory (I haven't studied the list hard enough to work out whether they actually do). She later emphasises this by adding: "Above all we were looking for endurance in both work and influence; sometimes the latter operates more stealthily than the former, and lesser-known names come to the fore." Whatever that means. It sounds like an abdication of responsibility on the part of the critic, along with a bit of mystical blue-smokery to cover her retreat.
Hmm. Philip Larkin I admire a great deal as a poet. And he very nearly married my aunty. But the greatest British writer since 1945? Surely not! And my C. S. Lewis fannishness is well documented in these pages, but in at No. 11? I do love the Narnia books, and I'm in awe at the quality of the man's mind, but he would have scoffed at the idea that he was a great writer, and so do I. *scoffs* [ETA: That sounds a bit ungenerous. I do think him a very great man of letters.]
Interestingly, that typically British writer, the crime novelist, seems (as far as I can see) to be entirely unrepresented here.