England and Cook failed to reinstate a Liverpool goal disallowed by offside because they thought it had already been given.
Referees body PGMOL has admitted the mistake and confirmed the two officials have been replaced on duty for Nottingham Forest v Brentford on Sunday and Fulham v Chelsea on Monday.
PGMOL has said Diaz’s disallowed goal should have stood at the Tottenham Hotspur Stadium following a “significant human error”.
England has been replaced as the fourth official for Sunday's Premier League game between Nottingham Forest and Brentford. Cook has been replaced as assistant referee for the game between Fulham and Chelsea on Monday.
In a statement on Sunday, PGMOL said: “Darren England and Dan Cook have been replaced for the Nottingham Forest v Brentford and Fulham v Chelsea matches.
“Craig Pawson will now assume England’s duties as 4th official at City Ground while Eddie Smart will take over from Cook as assistant ref at Craven Cottage.”
Diaz's goal was ruled out following an unusually quick VAR check, in which the customary offside line graphic was not shown.
PGMOL said on Saturday: “PGMOL acknowledge a significant human error occurred.
“PGMOL will conduct a full review. The goal by Luiz Diaz was disallowed for offside by the on-field team of match officials. This was a clear and obvious factual error and should have resulted in the goal being awarded through VAR intervention, however, the VAR failed to intervene.”
Liverpool, who also had Curtis Jones and Diogo Jota sent off, lost 2-1 after a stoppage-time Joel Matip own goal.