Alastair Cook has revealed England's players were "curious" about Australia potentially engaging in ball-tampering during the recent Ashes series.
The shamed trio claimed that was their first instance of ball-tampering.
But the spotlight has now been put on the Ashes, with television footage since emerging of Bancroft putting sugar in his pocket.
Australia's consistent ability to get reverse swing had England's bowlers scratching their heads during their 4-0 series defeat.
Cook was part of the England side and he admitted on Tuesday that there were questions among his squad about the third Test in Perth.
Asked at a Chance to Shine event in Tunbridge Wells whether England suspected Australia of ball-tampering during the Ashes, he said: "Yes a little bit, certainly in Perth when the outfield was wet with rain they got the ball reversing.
"I didn't see anything. We have been pretty good at managing the ball to see if we can get it to reverse swing but then there's the thing with the quicker you bowl the ball it reverse swings more.
"That was the thing in 2005, we had Simon Jones and Freddie (Andrew Flintoff) who were quicker than the Australian bowlers.
"We have to be very careful, we were curious at certain moments but then we couldn't get the ball up to 90mph where they consistently could."
Australia's actions in Cape Town were widely criticised, with Smith and Warner both receiving year-long suspensions.
Cook insisted that should be a timely reminder for the game to be played in the right way.
"It's not for me to comment on punishment, but the whole thing is a reminder that people want to see," he said.
"It's the same with cycling, that whoever is playing that people play in a fair way. If you try your hardest and there's no external things that you win or lose that way.
"It's amazing the public outcry for that.
"Sometimes with the pressure of playing, and it is so important to you and it's your livelihood, sometimes winning or losing can overtake things.
"It's wrong for everyone to sit in the cold light of day and criticise because people do make mistakes."