New Zealand led 2-1 in a best-of-five one-day series in 2015, but England rallied to win 3-2 in one of the most memorable international series in recent times.
The two will meet again this summer after being drawn with Australia and Bangladesh in Group A, and Williamson is adamant his side will repeat the attacking brand of cricket it displayed two years ago on English soil.
Williamson is set to lead New Zealand into his first major 50-over tournament as captain, having taken over the reins from Brendon McCullum in 2016. And the 26-year-old has fond memories of the last time he took on England away from home, although he insists it will have little impact on the result when they meet next week.
"Any time you have those experiences against opponents you are coming up against in similar conditions, it is the same side too, it is only a good thing," he said.
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"But there is not much time for slip-ups or conservative cricket."
In contrast to the World Cup, the Champions Trophy does not allow sides to start slowly.
New Zealand open against Australia at Edgbaston on June 2 before tackling host England at Sophia Gardens in Cardiff four days later.
And Cardiff is the scene again for their final group game, against Bangladesh on June 9.
"It is such an interesting tournament because it is such a short tournament," Williamson said.
"It is a very interesting tournament having played in it before and everyone is a real contender so you need to play with freedom, be prepared to take the game and hope things land in your favour."
England and South Africa have dominated all the pre- tournament talk, but New Zealand like flying under the radar.
They are currently fourth in the ODI rankings and have reached two previous finals - emerging successful in 2000 before losing to Australia in 2009.
"The exposure and learning that can be done there, it is a huge tournament so the more the merrier. It is a great competition to be part of and we push for as many players as we can to be involved in the IPL," he said.
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