New Zealand coach Mike Hesson warned England on Wednesday not to treat his side as the starter before they tuck into the main course of the Ashes series against Australia.
England host New Zealand for two tests, the first at Lord's starting on May 16 and the second in Leeds on May 24, before playing back-to-back Ashes series later this year.
"These are two hugely important test matches for us," British media quoted Hesson as saying. "We're making progress as a test side and certainly won't like to be the entree for the main course later in the season.
"England's record in England in recent times has been outstanding. It's a tough place to tour and we know that we've got to be on the top of our game."
The tour also includes three one-dayers before the International Cricket Council's one-day Champions Trophy tournament and ends with two Twenty20 internationals.
It comes less than two months after underdogs New Zealand drew a three-test series against England at home, having got to within a wicket of achieving a remarkable 1-0 series victory over the world's second-ranked side late on the final day.
"I've tried to forget about that game to be honest, especially the end of it," Hesson said.
"We felt we dominated but that's the game. These two tests will be tough in very different conditions. We gained a lot of confidence, but it was a series in isolation and we can't get carried away."
England batsman Kevin Pietersen did not play in that third test because of a knee injury and has been ruled out of this month's two tests, the one-dayers and the Champions Trophy, which is welcome news for New Zealand.
"KP played against us in the first two tests and missed out on the third and to be fair we weren't unhappy about that," Hesson told Sky Sports News.