As part of just-announced education reforms in Australia, these subsidies would be withdrawn and New Zealanders would become full fee-paying students.
However, they could be given access to student loans, which have been off-limits for most expat Kiwis until now.
The proposals will require a law change and, if passed, will come into force in January next year. Students already enrolled in courses would not be affected.
"We're pretty unhappy about it," English told reporters ahead of a National Party caucus meeting this morning.
"It shows what happens when you've got government deficit. The Australians are trying to sort out their budget and this is one area where they think they can make some savings."
Newly appointed Foreign Minister Gerry Brownlee will travel to Australia in the next week to meet his Australian counterpart Julie Bishop.
He would be "conveying our unhappiness" about the proposed changes, English said.
"We want a serious discussion with them about where they're headed with this policy, rather than announcements that are made either without telling us or at short notice."
English was not told about the proposals when he spoke to Australian Prime Minister Malcolm Turnbull on Friday, just days before the tertiary education reforms were announced.
On that occasion, English was speaking to his opposite about another Australian policy change made two weeks ago in relation to citizenship rules, which also caught New Zealand officials off-guard.
Brownlee said it was important to first get an understanding from Bishop about the extent of the changes and how many Kiwis they would affect.
"We've got to know exactly what the deal is. One of the most significant changes is around the student loan facility inside Australia, which may be of great help to New Zealanders studying there."
There were currently 8000 New Zealanders studying in Australia, and 6000 of them could be captured by the change, he said.
Brownlee also wanted to know whether there were any more changes to come which could affect Kiwis.
"For decades we had an arrangement where pretty much each country treats the others as if they were citizens," he said.
"We've had changes continuously since 2002, this is another evolution along the way."
'Bromance' over
Labour's education spokesman Chris Hipkins said the transtasman "bromance" enjoyed by former Prime Minister John Key and Turnbull appeared to be over.
The Australia Government had "walked all over" New Zealand again, he said.
"So much for the close transtasman relations that National like to talk up. How can Bill English allow himself to be blindsided by this, especially after he had a discussion with Malcolm Turnbull just last week about immigration changes?"
Asked why he did not clamp down on Australian expats, English said he preferred to maintain a positive relationship and seek better conditions for expat Kiwis rather than make a knee-jerk reaction for "short-term satisfaction".
"That's better than a mutual arms war to see who can treat each other's citizens worse."
Access to loans
A paper outlining the Australian education reforms said that while New Zealand citizens received subsidised study in Australia, they were unable to access student loans in Australia.
"This reform will address this anomalous situation by extending loan support to such permanent residents and New Zealand citizens and removing access to [subsidised study fees], effectively treating these students the same as domestic full fee-paying students."
Oz Kiwi spokesman Tim Gassin, whose organisation advocates for expats in Australia, said fees would rise by 300 per cent to 500 per cent if the proposals went ahead.
Gassin said the changes could also put pressure on the New Zealand education budget because many expats would return home to study.
Under a transtasman deal in 2015, student loans were made available to special category visa holders who went to Australia as dependent children and had lived there for at least 10 years. About 2600 New Zealanders became eligible for loans under the deal, which came into force in January last year.
This group would remain eligible for what are known as Help loans under the proposed reforms.
Australians can get access to student loans in New Zealand if they have lived here for three years.
Med students hit hardest
The proposed changes could hit people wanting to study law or medicine the hardest. They would face fee increases of more than 400 per cent.
Father Shyam Mathur, who lives in Auckland, said his 16-year-old daughter Inashi was in Year 12 and wanted to study law or medicine at an Australian university, where more places were available than in New Zealand.
If the proposed changes went ahead, her tuition fees would rise from about $11,000 to about $60,000.
"So obviously it's going to impact that decision. Student loans are not interest-free as they are here in New Zealand.
"Assuming she does medicine or law, it is going to put her back $300,000 or $400,000."
Mathur's eldest daughter Shyamolie is in her third year studying medicine at Monash University in Melbourne. She is unlikely to be affected by the changes because she is already enrolled.
The NZ students' union said Australia's Higher Education Reform package created a double standard.
"New Zealanders will be left short-changed as a result of these changes, forking out thousands more dollars to study in Australia," national president Jonathan Gee said.
Gee urged the Government to lobby Australia to restore access to domestic fees for expat Kiwis.
The educations reforms in Australia come two weeks after Australia tightened its citizenship rules.
While many expat New Zealanders would be exempted from those changes, those who arrived after February 2016 will face a more difficult path to citizenship.
Australia-NZ changes
2001: Australian Government removes access for NZ expats to unemployment and sickness benefits, while keeping access for child-related and family benefits. Direct pathway to citizenship removed for Special Category Visa (SCV) holders.
Oct 2015: SCV holders given access to student loans, beginning in January 2016. All other Kiwis expats have no access to loans.
Nov 2015: Australia introduces hardline law change, which revokes the visas of some ex-criminals no matter how long they had lived in Australia.
Feb 2016: Australia says New Zealanders who arrived between February 26, 2001, and February 19, 2016, who have earned more than A$53,000 a year for five consecutive years will be able to apply for permanent residence and citizenship, from July 1, 2017.
April 2017: Australia says applicants for citizenship must have been permanent residents for four years, rather than one year. Kiwis on the special pathway to citizenship announced in 2016 are not affected.
May 2017: Australia proposes withdrawing subsidies for NZ citizens studying in Australia. NZ citizens would pay full tuition fees but would be given access to student loans.
AUSSIES IN NZ: Are entitled to Jobseeker Support, Sole Parent support and Supported Living after a two-year wait; extra assistance such as accommodation supplement and disability allowance if they are resident in New Zealand, working for family tax credits, student loans after a three-year wait and are eligible to vote after 12 months of continuous residence.
