Mr English said first home-buyers would benefit from measures in the Budget which supported growth. But there were no specific measures planned for this demographic.
The minister reiterated that money alone would not solve Auckland's housing problems, which were primarily caused by restrictive planning rules.
The Government has indicated that it will force the Auckland Council to change its urban growth limits if councillors refuse to do so in the Unitary Plan.
These limits were also affecting the Government's attempts to expand social housing in collaboration with NGOs, Mr English said.
"The issue particularly in Auckland is not a lack of finance, it is a lack of houses.
"We can pay for all the houses we can procure. The limitation is how many houses are available and suitable for social housing."
Social Housing Minister Paula Bennett said the social housing announcement in the Budget would show people how hard the Government had been working on the issue.
She dismissed a suggestion the Government was scrambling to address the problem, after recent media stories highlighting people living in cars and garages in Auckland.
"No, I have been working on this policy since I became a minister, so it's been 18 months.
"You saw announcements last year, we made some significant changes - put more money into emergency, put more money into rebuilds.
"We now have one of the highest rebuilds within Housing New Zealand that they have ever had... Trust me, I have been working really hard every single day since then.
"What you will see in the Budget this week will back up that there is a lot of work happening."
The increasing unaffordability of housing in Auckland has led Oppositions parties and others to reiterate calls for a state-sponsored building programme.
Labour leader Andrew Little said Labour's policy was to drive a huge building programme through Government.
"When Auckland is about 40,000 houses short of what they need, you have got people who are homeless, you've got first home buyers...who simply cannot get into a first home, we are at a point now where the Government must lead the way - lead a house building programme."
Prime Minister John Key said house-building by the Government was a "misplaced" idea.
"We've long since given up doing that. The Ministry of Works used to be the provider of roads and schools and houses in New Zealand and it wasn't a very successful model."