Here is a theory I made up myself.

PART I: Linking Robin Hood and Bedknobs and Broomsticks
This is the easiest part of the theory, and you can take it by itself even if you don't believe the other parts. In the beginning  of Robin Hood, what have we got ? First a human narrator tells the beginning of the story of the "real" Robin Hood. Then Alan-A-Dale shows up and tells the spectators that there have been many legends about Robin Hood, but that "here in Animals Kingdom they have their own version", and then that "here is what actually happened in Sherwood Forest". The first important parts here are:
  • All that story that we are about to see happened in Animals Kingdom.
  • This is the truth (or either Alan-A-Dale is a lyer).

Then, just after seeing the openeing credits, there are plenty of anthropomorphic animals. (Oh, by the way, this has nothing to do with the theory but did you notice that in Robin Hood, the Sherwood people and Robin and Little John are european and north-american animals (turtle, bear, badger, fox, rabbit…), while the army of Robin Hood is entirely made of tropical animals (snake, lion, hyena, hippopotamus, elephant, vulture…) ?), living in a medieval-looking world ruled by an anthropomorphic lions dynasty, but with more of different species than in the Mickey Mouse universe ? And no humans at all ? 

Does it remind you something ? Why, Naboombu of course ! Then, how, will you ask me ? Here I have different ideas in mind. Either: this is the bare truth and it happened long ago (and John and Richard are more or less far away ancestors of King Leonidas, and the bear you see inthat screencap is a descendant of Little John); this is the bare truth and it happened recently (supported mainly by the modern-looking prisoner suits at the end) and in that case King Richard died shortly after the ending of Robin Hood and King Leonidas took the throne; or Alan-A-Dale was lying when he said it was the truth, and this is only how the Naboombu citizens tell the story of Robin Hood, that they probably learned from a human visitor at one point. 

Part II: Linking the stuff with The Jungle Book
Here, this is mainly supported by the thing you see on the right: 

Because here you can see Kaa. Yes, here. In pink. PINK ? you say. Yes, pink. Keep your calm, this is very simple. What seems obvious to me in that scene is that the animator intended all that to be cameos of Kaa, upcoming Little John — or either Baoo — and Archimedes the Owl (behing the Bear's flag). But the guy who done the paintings did not notice it: that's how Archimedes turned blue, Little John's green shirt turned orange, and… Kaa turned pink. (Actually, aside from don't recognizing Kaa in particular, why did this colorist done a pink snake ? At least, a green snake, please ! mercy !) Also, you see ond of King Louie's monkeys before the football match.

And in The Jungle Book you see animals who act partially like humans, partially like animals. The best example being Hathi who do everything like a human colonel. And Louie ? Interesting case: he wants to be more human than he already is. Do you remember was Astharoth was intending to do in Bedknobs and Broomsticks: turning the animals into humans. Apparently, as soon as they were half-human (a.k.a. anthropomorphic animals), the animals refused to go any further, killed Astharoth and escaped. Maybe Louie is sad that his ancestor did so, and would have liked to be completely human? Also, we may argue that Astaroth done the animals one by one, leading to some of them being more anthropomorphic that others who were just "begun" when the most anthropomorphic revolted. That would explain that we have both quadrupede elephants in The Jungle Book and bipede elephants in Robin Hood and Bedknobs and Broomsticks.

Then you have the main bother: brhm… don't you remind that at one point, it is stated that humans are forbidden in Naboombu ? So, well, the human village at the end of The Jungle Book ? Ooooh… Well… I need your help on that one, but I have one or two bases:

  • The anthropomorphic animals' jungle is separated from the village by a river. You don't see any humans in the jungle, and no animals in the village. 
  • In Bedknobs and Broomsticks, the Bookseller states that the only human to have been on Naboombu was an indian. Must I remind you: Mowgli's indian and has lived with the anthropomorphic animals. 

So perhaps Naboombu is not very far from India, and actually the river was the sea… As a metaphor… I dunno… Does anyone have an idea ?

Problems with the theory

I am very proud of my theory, but I see very well that there are still some problems. For example, I had in mind to include the Mickey Mouse Cartoons universe to the mix (because of Sport Goofy in Soccermania and with the cameo of the Naboombu football players and Mickey's Christmas Carol  with the Robin Hood characters' numerous cameos) but I have the following problem: and all these stories with Mickey or Goofy or Donald going to far away country and there meeting other anthropomorphic animals ? And also, there is much more technology in this universe than in the original Naboombu ? And the stories in which the characters state that they live in America ?… Also, other thing: I don't manage to explain convincingly the appearances of the Fox and the Pig from Mary Poppins in Bedknobs and Broomstick, because of the humans you see in their original world. 

Oooh, perhaps I'm bothering too much about quick cameos. But still, I remain 100 % of the first part. What do you think of it ?