"The delays in deciding revocation requests undermines the department's policy of giving primary consideration to the best interests of those who have young children and/or experience prolonged family separation," Commonwealth Ombudsman Colin Neave said.
English is in Europe for his first official trip as Prime Minister, and told reporters he had not been briefed on the new report.
There was "ongoing discussion" with Australia on the deportation issue, he said.
"There has been a lot of progress made in the last couple of years, particularly with Prime Minister Turnbull, making sure the Australian system pays attention to it. Pipelines are better. But there will be ongoing issues."
The Government has put more money into Corrections and other services to cope with the high number of deportees coming from Australia, many of whom have few family links here and are at high risk of re-offending.
Former Prime Minister John Key hosted Turnbull in Auckland in October 2015, and pushed for the threshold at which Kiwis were deported to be softened.
That should be done in recognition of the special relationship the two countries have, Key argued.
However, Turnbull declined, saying it was Australia's "absolutely legitimate sovereign right" to revoke visas should the holder commit a crime.
He promised to put more resources into the appeal process so it could be carried out more quickly, and to clear a backlog that had resulted from the law change in December 2014.
However, the number of New Zealanders held in detention centres has not declined significantly since then.
As of November 30, 1414 people were in Australian immigration detention centres such as Christmas Island. Most - 13 per cent or 184 - were New Zealanders. The next most common nationality was Iranian.
In October 2015, 213 Kiwis were being held.