"London is obviously covered in the London, England and Great Britain books. And England is covered in the GB book."
Yep, that's pretty much correct. But technically, here's the catch: the Great Britain book has somewhat less coverage of England than the England book.
What Rick's editors did not do, in creating the Great Britain book, is: they did not simply copy every page from the England book and paste them into the Great Britain book, and then add Wales and Scotland.
Some travelers will consider the difference in coverage to be unimportant, others might consider the difference to be significant, given their preferences and exactly where they're going in England.
Also, note carefully that none of the four books mentioned were intended to cover every worthy location in the UK or Ireland, Rick is selective in his coverage, and in that regard his books differ from the competitor books.
Since it gets down to a matter of your personal preference, perhaps the best way for you to decide is to go to your local bookstore and browse through both the Great Britain and England books; and then decide whether, for your needs, the coverage of England in the Great Britain book is sufficient for your needs. If it is, you'll only need the two books, Great Britain and Ireland.
In my opinion, you don't need the London book, if you're going to buy either the England or Great Britain books. So we've at least eliminated one of the four! :)