it's advocating actions which are illegal in the UK
Firstly, that isn't of itself the basis for banning books under any UK legislation. So even if it were advocating illegal activity, that does not make the book illegal unless it breaks other legislation. Shooting people with your illegally held handgun is a good way to go to jail, but this book is clearly not illegal to sell, buy or possess. Even if you happen to have a shotgun certificate, you'd probably be wise to ignore the advice here, too.
Secondly, from what I've read of the book, it's not at all clear that the measures it proposes (as opposed to what child abusers have taken it to propose) are illegal in the UK. Section 58 of the Children Act 2004 is pretty widely drawn. It would require a UK prosecution of someone for following the book's precepts, but not going beyond them, to settle that question. I suspect that the CPS would have very little appetite for bringing such a prosecution even if it would get on to social services' radar. They have bigger fish to fry.
just some very emotive coverage on the death of a child supposedly as a result of following the advice in the book
Sure, it's a thoroughly nasty book, and it says a lot about fundamentalist "Christians" that so many of them have been drawn in by it (seattletimes.com/html/localnews/2016875109_hana28m.html). The world would be a better place if books like this, and indeed their authors, didn't exist. I think people that punish their children physically should be shunned, although I think that the unintended consequences of trying to make it illegal completely would be susbtantial. But "yuck" isn't the basis for banning books.
The argument advanced upthread that someone might accidentally buy it while sleep deprived and be so overwhelmed by the power of its persuasive prose that they set about abusing their child is laughable. It's essentially the "is this a book that you would want your wife or servants to read?" argument fifty years after the Chatterley trial: "I can see this book for the trash that it is, your honour, but there are some people without my education and discernment who might be corrupted by it". Aside from anything else, it also requires that rather than Googling for advice people carefully trawl for books and wait for the postman to arrive.