Avant said that if a housebuilder fails to increase output by a given percentage in one year, its access to Help to Buy subsidies should be reduced the following year.
Avant's CEO Colin Lewis said it is time for Government subsidies to help home buyers who need them rather than boost housebuilders' profits.
"Help to Buy is a useful tool. It's supporting the availability of homes, but not to the extent it could," he said.
"Someone buying a £600,000 home in the South East surely doesn't need Help to Buy to subsidise them."
He said it was up to the Government to do its research and set a target for increased output.
"At the moment Help to Buy is working for the benefit of housebuilders and it should be for the benefit of home buyers," he added.
"Scotland has reduced their limits on Help to Buy to £200,000 per home. That's a good starting point."
The Government has come under fire for using taxpayers' money to promote Help to Buy, which has boosted profits at the major housebuilders, leading to protests about bonuses at firms like York-based Persimmon.
"Help to Buy has helped many home buyers to get their foot on the ladder, but the fact remains that the UK is still facing a severe housing shortage," said Mr Lewis.
"If we are to continue with this valuable initiative, changes must be made to rebalance the benefits of the policy to home buyers and away from housebuilders. Let’s link the availability of Help to Buy funds for housebuilders to an increase in the numbers of new homes they build."
Mr Lewis said that Avant is keen to play its part and the group aims to double its production to 4,000 homes a year by 2023. He said the obvious areas for more housing are between Sheffield and York, the North West, the Midlands and Scotland.
The average price of an Avant home is around £260,000 and the group is keen to target the sub £200,000 market by introducing a range of smaller footprint homes which it can offer to customers at a lower price point.
"We expect this new range to sell for £175,000 to £185,000," said Mr Lewis.
"These are two, three and four bedroom houses that are built with a more cost effective design. They are for people who want an Avant home but can't afford it. They are smaller houses and simpler to build."
The firm has carried out a trial of these cheaper homes at two sites in Scotland.
"Our customers love them," said Mr Lewis.
"We are looking at a number of locations around the country. We will have opportunities in Yorkshire."
The plans were announced as Avant reported strong growth and said it is on track to deliver its current target of delivering 2,000 homes per year in 2018, one year ahead of schedule.
The group said it is set to deliver record volumes in the current financial year as it is fully sold for this year with two months of the financial year to go.
It said it is on track to deliver in the region of 25 per cent revenue growth and expects to end its financial year to April 27 with 70 outlets, up 40 per cent on the 50 outlets in April 2017.
"We have made exceptional progress in growing our business over the past few years thanks to our relentless focus on offering aspirational, customer-led homes in prime locations across the Midlands, the north of England and central belt of Scotland," said Mr Lewis.