An estimated 385,000 families with children are expected to be on average of $75 a week better off in 2020-21.

New Zealanders on benefits are now better off - but some say they're only getting an increase of $3 a week.

The accommodation supplement was boosted on Sunday, one of the first priorities of the new Labour-led government.

Increases vary from family to family. However, some said after April 1 they're expecting only a $3-$10 increase, according to their MyMSD payment forecast.

Your experience of receiving a benefit Share your stories, photos and videos. Contribute

They said it was not enough and wouldn't even cover the ever increasing cost of food.

READ MORE:

* Minimum wage set to jump to $20 by 2021

* Rich oldies should not get the state pension

* Minimum wage workers set for 75 cents an hour pay rise

Accommodation Supplement and Accommodation Benefit increases were announced in the 2017 Budget under the National-led Government, and are part of the government's wider Families Package.

CAMERON BURNELL/STUFF New increases to accommodation supplements and a minimum wage boost will be in effect from April 1.

The package, when completely implemented, aims to significantly reduce child poverty.

But Kaleb Holmes, who was expecting an increase of $6, said the benefit increase was not enough for basic needs.

"The amount they are suggesting is far from bringing a far out-dated benefit system up to current market value ... food alone has increased more then $6 in the last 3 years."

The price of weekly fresh fruit and vegetables had increased more then $6 for a weekly shop.

"I find the new increases to be a cruel joke."

Cherie Grant was expecting an increase of $3, and said it was not going to help her family of seven.

She called the changes "fake promises" from the government.

"A $3 increase is not going to help many families."

A Child Action Poverty Group media spokeswoman said the increase was good, but there was still a significant amount of change needed to reduce poverty.

"There's still a lot that needs to be done for the families that are in the lowest of incomes."

Some may not see a significant change until the rest of the Families Package came in to effect, after July 1, she said.

The increase of this weekend would not go far enough to help people on low incomes to cover basic living costs, she said/

The Families Package includes introducing the Winter Energy payment, increasing Best Start payments, and an increase of paid parental leave to 26 weeks.

Around 41,000 students would get an extra $20 a week from a boost in their accommodation benefit after the changes.

The changes to the accommodation supplement are one of two major changes being introduced by the government on April 1.

On Sunday, the minimum wage lifted 75c to $16.50 an hour.

The new Families Package was part of the Labour-led Government's 100-day plan and was designed to provide targeted assistance to improve the incomes of low-and middle-income families with children.

*Comments on this article have now closed.