I think it would generally be accepted that the top four clubs in English Football are Arsenal, Chelsea, Liverpool and Manchester United.
Listed below are major shareholders in these clubs
Arsenal - Alisher Usmanov (Russian Oligarch)
Chelsea - Roman Abramovich (Russian Oligarch)
Liverpool - George Gillett and Tom Hicks (American Businessmen)
Man Utd - Malcolm Glazer (American Businessman)
As I understand it all but Alisher Usmanov effectively "own" the clubs, he is the 2nd largest shareholder (again as I understand it) with around 23% of the shares, which he purchased for £120,000,000.
In addition to this Manchester City are owned by Thaksin Shinawatra, the former Thai Prime Minister. Lakshmi Mittal (Indian Businessman) has recently bought a substantial holding in QPR and there's no sign of this trend letting up. It seems to be the fashion to buy an English football club.
So the clubs aren't owned by Englishmen any more, so who's managing them. Not really any need to go into that, the top clubs aren't managed by Englishmen and haven't been for some time.
So, how English is English club football. Not very it would seem.