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Mr English, speaking on Tuesday, suggested council planning policies were restricting the availability of land, driving up house prices and ''causing poverty''.
Dunedin Mayor Dave Cull yesterday criticised the assessment as ''simplistic'' and ''unhelpful'', saying there was enough land, and more changes in the pipeline, to cater for growth in the city.
The council's development contribution charges were also only ''about half'' the national average, and it was ''odd'' to link poverty and restrictions on new housing, he said.
''It's an unhelpful generalisation ... new homes aren't even within the hopes of people at the bottom of the economic ladder,'' he said.
Other southern mayors had mixed views when contacted by the Otago Daily Times yesterday.
Some agreed the cost of housing was part of the poverty problem, but took exception to being singled out, while others said new ways to free up land, or in-fill areas, were already being considered.
Queenstown-Lakes Mayor Vanessa van Uden said her council faced one of the biggest housing affordability problems in New Zealand, outside Auckland and Christchurch, but was working to address it.
That included work on a new housing accord to improve the supply and affordability of housing, and district plan changes already being considered.
That could mean new rules allowing smaller sections or higher buildings to cater for growth within existing boundaries, while protecting what was ''special'' about Queenstown and Wanaka, she said.
What was not helpful was ''putting the blame on one particular party'', she said.
''We are not ignoring the problem and hoping it will go away.
''We are all in this together - central government, the people who want in houses, us, and the developers.''
Central Otago Mayor Tony Lepper acknowledged councils were contributing ''slightly'' to housing costs, ''but by far the biggest costs still [come from] stuff we're doing for central government''.
He was encouraging Central Otago District Council staff to ''really, really look'' at its district plan, which was being reviewed, and see if there were new ways to free up land and reduce housing costs.
That could come through smaller sections or more rural land being rezoned for residential use, although simply rezoning land ''out in isolation'' would not be the answer, he believed.
Doing so would only add to the cost of connecting new services, paid for through development contributions, which would, in turn, drive up the cost of those homes, he said.
''I think it's a mixture. We can't duck all the blame. We've got to get in there and have a look and see if there's anything in there we can help with.''
Waitaki Mayor Gary Kircher said there were ''a lot of different reasons'' for poverty, including housing affordability, ''but it does vary across the country''.
''If he [Mr English] is saying councils have more responsibility for this current state we're in, I'd disagree.''
Housing in the Waitaki District remained ''reasonably affordable'' and the council was working to open up new areas.
It was also reviewing its district plan and development contributions policy.
Clutha Mayor Bryan Cadogan was not available for comment yesterday, but council staff there said district's housing was ''generally affordable'', with ''no significant impediments ... delaying new builds''.
Their comments came after Radio New Zealand yesterday reported Mr English, speaking at release of the Government's books for the last financial year, said inequality would have decreased if not for councils' poor planning.
The cost and complexity of getting permission to build a house was the biggest single contributor, and was having a ''pretty devastating'' impact on families forced to spend up to 60% of their income on housing.
''So councils need to understand that when they run these policies that restrict the availability of land and the opportunity for lower value housing, they are causing poverty,'' Mr English said.
Invercargill Mayor Tim Shadbolt, also contacted by the ODT yesterday, said: ''I saw that - blaming us on housing.
''Well, last time they said we had too much red tape, they built a whole lot of leaky houses.''