Williamson missed Wednesday's second match of the five-match series, in which the tourists eased to a series-levelling six-wicket win, and was replaced at No 3 by Mark Chapman - winning his first ODI cap for the Kiwis.
A slight hamstring strain kept the captain out, with Tim Southee leading the team instead, while Taylor then suffered a quadriceps injury mid-match and was unable to field.
New Zealand Cricket issued a brief update after training on Friday which read: "(Ross) Taylor has been ruled out of Saturday's third ODI against England.
"He will be further assessed ahead of the fourth ODI. (Kane) Williamson passed his fitness test at training and is available for the third ODI tomorrow."
Another key player who will also be involved, and has had a significant impact in both matches so far, is all-rounder Mitchell Santner.
He followed his big-hitting 45 not out which clinched the series opener in Hamilton with his first ODI half-century in his 50th match at Mount Maunganui two days ago.
It was not enough to keep the Kiwis in front, however, or extend their winning streak to equal the national record of 10 matches.
"We were outplayed, especially the way they bowled up top and didn't give us much," said Santner. "We lost wickets at crucial times, and 220 was never enough on that surface."
He can hope for much better at the Westpac Stadium, a venue where New Zealand trounced England at the last World Cup and also beat them in last month's Twenty20 Tri-series.