The company is operating in a New Zealand plasterboard market which is dominated by Fletcher Building.
Twyford said building materials competition was essential to lowering costs and he urged the Commerce Commission to release the findings of its investigation into the wallboard market, first announced in August last year.
But Nick Smith, Building and Construction Minister, said while wallboard market dominance was being investigated, politicians needed to stay out of it.
"It's well-established that ministers or MPs shouldn't be interfering in the independence of the commission," Smith said.
Last week, legislation was introduced to amend product setting standards after criticism from importers about getting products approved.
"There's been a concern that the standards process has been excessively dominated by the current players and we need to stay at arms length," Smith said.
The Productivity Commission has criticised a lack of building materials competition, saying it cost as much as 30 per cent more to build a house here than in Australia. Twyford said Fletcher Building subsidiary Winstone Wallboard's 94 per cent share of the wallboard market was bad for the building industry, house buyers and the property market.
"Plasterboard is 41 per cent more expensive in New Zealand than Australia meaning it would cost $12,000 for a standard house in New Zealand compared to $8000 in Australia. The Government has totally failed to tackle the market monopoly," Twyford said.
Kevin van Hest, managing director of Elephant Plasterboard, which has 3 per cent of the national market, said suppliers were shy about stocking or selling alternatives to Winstone's Gib because they had strong financial reasons not to.
But David Thomas, Winstone general manager, said the business only had a 94 per cent market share because it manufactured and delivered the best product to customers.
"People do have other options and they have had for the last 20 years," Thomas said, citing Elephant Plasterboard and other products including Chinese-manufactured board.
Last year, the Government limited Fletcher's plasterboard power by giving German company Knauf a chunk of a $40 million plasterboard supply deal for the Christchurch rebuild.
Philip King, Fletcher's group general manager of investor relations and capital markets, said high land prices were responsible for expensive Auckland housing. "The cost of plasterboard as a building material is a small percentage of the total house cost. Winstone Wallboards has co-operated fully with the Commerce Commission in its inquiry into plasterboard," King said.
Smith said he did not know when the commission's findings would be released.
See Knauf's statement here: