Well taking things a step at a time, things are looking better to me. Granted he may still be in "serious" condition, things could be far worse, especially with a 300 MPH crash.
The Times is pointing to a possibility that the violent shaking of his head, and thus his brain, probably caused swelling of some kind, causing Hamster to lose conciousness. Although we don't know the exact consequences of the crash on his brain, one can assume that there was some bleeding of some kind. The problem would be if the bleeding would continue, or the possibility of forming a clot of some sort as well.
...That said, the Times was reporting that Hamster was fully-awake and talking with not only people who were visiting him the hospital, but also the regular folks around him as well. That is indeed a good sign that nothing too severe had occoured, atleast not enough to cause brain damage, so we could see Hamster back (although in limited appearances) to Top Gear in time for the debut in October.
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Linky to the Times Article)
Interestingly enough, the article points twards Sterling Moss' crash in 1962 that had many of the same issues arise. Although he was unconcious for several months, he for the most part was alright, although his memory deminished just a bit. Thankfully with modern medicine and advanced safety equipment, it appears as though Hammond won't be in the same boat per-se.
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...And even then, if he can't get the help he needs in the UK, I'm sure that his family would be looking for the best neurological units in the world. Many of them are indeed here in the US, and I'm positive there are some excelent facilities in Germany and Sweeden as well.