In the end, the decision was left to the television match official who ruled that Williamson was not out.
While England players were unhappy at the time, coach Trevor Bayliss wasn't getting too worked up about it.
"Everyone knows Woaksey, he's not a bloke who would cheat a bloke out," Bayliss said after the game.
"I would have liked to see us appeal a bit harder. But look, that's the game. Decisions are right and wrong in the history of the game, we've just got to get on with it."
New Zealand lead by 117 runs with 7 wickets remaining in the innings.
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