They don’t have the power directly but the FA, as the governing authority in England, oversees certain regulatory and administrative duties in relation to English clubs.
They can raise fees are certain duties/rewards if they so wish. That’s what Gary was talking about. That kind of practice is unheard of because no one expected English football to generate such wealth.
I’d be in favour of coming up with mechanism designed to siphon money from the biggest clubs transactions with the intention of reinvesting directly to grassroots sports.
The Govt could also use legislation to compel the PL is give a greater amounts to grassroots endeavorers, it dirty tactics for sure but there are many ways the Govt can stifle the PL operation tbh in order to get them to give more