"National said at the time, and she has repeated it since, that it was about increasing parental choice, when it was really about cutting costs. The truth has finally come out."
But an aide memoire to Hipkins from the Ministry of Education dated November 24, released to Kaye under the Official Information Act, shows that even National's changes were expected to increase the cost to taxpayers.
Until last year, all schools were required to accept any child after they turned 5. Although parents don't have to send their children to school until they turn 6, most children start on or soon after their fifth birthday.
National's change last year allowed schools to take children only in "cohorts" at the beginning of the term closest to their fifth birthday.
The aide-memoire says that change would have cost taxpayers an extra $8.3m a year if all schools had adopted cohort entry, because the number of children forced to wait in early childhood centres for up to two months after their fifth birthday was expected to be more than the number starting school before they turned 5.
Hipkins wants to keep the change allowing schools to take children only in cohort groups at the beginning of each term, or possibly also at half-term entry points - but only after children have turned 5.
The aide-memoire says that change "will impose greater additional ECE [early childhood education] costs on families and substantially increase government expenditure across ECE".
If all schools adopt cohort entry, with entry only at the start of each term, it says Labour's policy would cost taxpayers an extra $50.3m a year - $42m more than National's policy.
The extra costs arise from both higher subsidies to early childhood centres and higher childcare subsidies to low-income parents.
The aide-memoire says Labour's policy will require changing the childcare regulations, which set a maximum age for subsidies of 5 years and 28 days, as well as changes to the Education Act.
In practice, the costs of both parties' policies will be below the potential costs stated in the aide-memoire because not all schools are expected to adopt cohort entry. Only 51 out of more than 2000 primary schools have adopted it so far.
Hipkins has asked for submissions by Monday (March 19) on whether schools should be allowed to take new entrants at mid-term entry points, or only at the beginning of each term.
The aide-memoire notes that allowing mid-term entry "would reduce costs to the Crown" because children would start school sooner after they turn 5.
Under either National or Labour, schools will also still have the option of "continuous entry", accepting children at any time after they turn 5.