Hammers boss David Moyes, as well as players Josh Cullen and Issa Diop, had to be sent home from the London Stadium on Tuesday just over an hour before kick-off having arrived unaware that they had tested positive.
With testing not mandatory in EFL games (Premier League players and staff must be tested at least two days before any game), clubs have been left in the precarious position of having to travel to games without confirmed results.
The situation is only being made harder as capacity in laboratories is being taken up nationally with a spike in cases. The Hammers have no new cases to deal with ahead of Sunday's game against Wolves but face Everton in the Carabao Cup on Wednesday and could be heading north not knowing their test results.
"Normally the test results have come back very quickly," Irvine said. "The labs are finding a bit more difficult because of the amount of tests they are having to do for people outside football. They are being stretched to the limit. The tests on Wednesday took a long time to come back. It is a situation that is out of our control.
"Yes, we could find ourselves in a situation where we will be tested on Monday and we have got the game against Everton on Wednesday so we could be travelling to Everton not knowing the test results.
"The situation at the moment is that we have got no choice. That is what we are going to have to do, and what we will do, until somebody tells us something different is happening."
The Premier League and individual clubs introduced very strict protocols when players returned for Project Restart following lockdown, restrictions which remain in place for the new season.
Despite the three tests on Tuesday, the Hammers recording a clean bill of health when the squad was re-tested the next day is proof the steps being taken are controlling the spread of the virus amongst players and staff.
"There was a fair amount of fear and anxiety around us restarting training after lockdown," Irvine said. "I have to say that this time that hasn't been there and fortunately it has not been a step back in anyway by what happened the other night because we've very quickly had everybody re-tested and had the all-clear. People have been reassured by that.”