Football clubs can have as many foreign players as they like as long as they meet the FA's quota for the number of English/homegrown players in each squad.
Also, many English players are overpriced and/or overhyped. Some of them have a little success and then let the British media hype get to their heads, and their career stagnates.
How many English players are being actively sought after by the big clubs in Spain, Italy and Germany during each transfer window? Answer: zilch. Because they are not good enough.
If you want a club with almost all English players, you'll end up with something like Burnley FC.