Do we know that for sure Andrew? I haven’t seen anything that talks about sport in general with Brexit.
Well, it will depend on what sort of trade agreement is struck, if indeed one is – at the moment they're in a transition period where it's still as if the UK is in the EU.
But if there was to be no agreement, the UK would no longer be part of the EU's freedom of movement rules – having the right to work in Italy today means you have the right to work in the UK, but it wouldn't in such a scenario. As far as I'm aware keeping freedom of movement the same as it has been is off the table.
Note: I am not a trade expert.
Obviously there are a lot of EU area players in the Prem League. Pretty sure the Brits will allow some dispensation for visa players from the EU, if any footy club wants to sign them. Otherwise the Prem League would no longer be the strength that it currently is.
I. E. If the freedom of movement rules were very restrictive, they'd have an exemption.