Just to be clear in the PL you don't require any minimum number of homegrown players. You just can't have more than 17 foreign association developed players in a squad of 25. So you could if you wanted to have no English developed players and just have a squad of 17.
In UEFA competitions the rules are different, you have to have at least 8 home association developed players and 4 from your own academy.
You could go with just 17 players but how many clubs realistically do that?
Also on the note of HG players you say "English developed players" do you mean English players developed at club or players developed at English club? I know it's semantics but the rule is for the latter.