The Kiwis travel to England for two Tests after the teams played out a draw over three matches in New Zealand earlier this year.
Williamson, who stands in as skipper in the opening match on tour against Derbyshire on Saturday, said that the Black Caps should not be seen simply as England's pre-Ashes warm-up series.
"I don't think we're caught up in the Ashes at all," The Mirror quotes the 22-year-old as saying. "We don't have anything to do with the Ashes, so we haven't looked at it in any way like a warm-up.
"We're targeting these Test matches and all our preparation is going into them. Winning the series would be great, a huge success for us.
"We want to improve every game because we're a young side, but we know we can beat anyone on our day."
The first Test gets underway at Lord's on May 16.