Leeds player Peter Lines received a positive result on Tuesday morning and while Oliver tested negative the previous day, contact with his dad meant both players were dumped out of the tournament.
Oliver shocked Thailand’s Noppon Saengkham 4-1 in his first round match on Monday and had been due to face Anthony McGill in the second round on Wednesday, while Peter was set to play Luo Honghao in his first round on Tuesday.
But both McGill and Longhao will now receive byes to the third and second rounds respectively as both Peter and Oliver undergo periods of self-isolation.
Lines took to Twitter to express his frustration after the test and trace system forced his withdrawal from the Milton Keynes event.
He said: “I test negative I win my match a day later my dad then tests positive I didn’t spend any time with since Saturday morning.
“His test was Monday afternoon and now I’m out as well!! Fair one.”
All other players and officials received negative test results on Tuesday morning after both Stuart Carrington and referee Andrew Barklam received positive results on Monday.
Grimsby’s Carrington had come into contact with Newcastle potter Sam Craigie, meaning - similarly to Peter and Oliver Lines - both players also had to withdraw from the first Home Nations event of the season.
World No.113 Oliver and Peter, ranked 28 places above his son, will receive the full support of World Snooker as they undergo their periods of isolation ahead of the rest of the season.
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