There are numerous"fiddles" with players being employed by overseas companies and also selling their "personality rights " i,e, appearing in adverts etc to overseas companies so that the fees go overseas and are not /are lightly taxed here.
In the first instance the overseas company will pay a smaller (?) salary to the player to avoid tax. They are of course the owner of the employing company with their manager and spirit their untaxed gains away.
I don't know if British players can do this.
Overseas players will undoubtedly pay some tax here.How much depends on how low an amount the I.R. will accept as a salary knowing what the club is transferring overseas.