However, England were productive on their two-point attempts, making 12 of 25, compared to New Zealand's 4/11 effort, while the Ferns also received little support from their other shooters, who combined for just six points.
With England possessing a strong lineup filled with their usual internationals, they won the second half 21-4 to pull away for a deserved victory.
New Zealand had a better balance in their victory over South Africa.
South Africa could only manage eight points in their second-quarter power play, and trailed 18-15 at halftime. They never came any closer as New Zealand put on a polished performance.
However, the Ferns could not replicate that against Australia, falling into a 28-14 halftime deficit as Australia used their first-half power play. New Zealand opted to take theirs in the third period, but could only muster a meagre eight points, and Australia held on for an eventually comfortable 40-30 win.
New Zealand sit in fourth on the ladder, ahead of only the winless South Africa and Malawi. They play Malawi tomorrow, as well as the unbeaten Jamaica, with the top four teams qualifying for the semifinals.
The Ferns will likely need to win one of those two clashes to keep their title defence alive, before the playoffs take place late in the afternoon today.