Shell: list directories ordered by file count (including in subdirectories)

I've nearly reached my limit for the permitted number of files in my Linux home directory, and I'm curious about where all the files are.

In any directory I can use for example find . -type f | wc -l to show a count of how many files are in that directory and in its subdirectories, but what I'd like is to be able to generate a complete list of all subdirectories (and sub-subdirectories etc) each with a count of all files contained in it and its subdirectories - if possible ranked by count, descending.

Eg if my file structure looks like this:

Home/
  file1.txt
  file2.txt
  Docs/
    file3.txt
    Notes/
      file4.txt
      file5.txt
    Queries/
      file6.txt
  Photos/
    file7.jpg

The output would be something like this:

7  Home
4  Home/Docs
2  Home/Docs/Notes
1  Home/Docs/Queries
1  Home/Photos

Any suggestions greatly appreciated. (Also a quick explanation of the answer, so I can learn from this!). Thanks.