However, he said government remained satisfied with how the caps were working and there were no plans to revise them.
The Help to Buy 2021-23 scheme began accepting applications in December and started allowing completions in April.
It is restricted to only first-time buyers and has regional property price caps which set the maximum purchase price in each region.
The regional caps are aligned to the first-time buyer market and are all set at 1.5 times the forecast regional average first-time buyer price as predicted by the Office of Budget Responsibility, up to a maximum of £600,000 in London.
In a written question, Labour MP for Stockport Navendu Mishra asked whether the Ministry of Housing, Communities and Local Government (MHCLG) had assessed the effectiveness of the caps.
Housing minister Christopher Pincher (pictured) replied: “The caps were designed to support the purchase of properties that are more consistent with the wider first-time buyer market.
“This in turn helps optimise the resources available to enable purchasers to achieve the dream of home ownership. The government has reviewed the caps and continues to be satisfied they allow good availability of first-time buyer type properties in each region.”
Pincher admitted there will be “local hotspots within each region that are more expensive,” but argued the benefits outweighed the restrictions.
“However, the approach is aimed at striking the right balance between better targeting the scheme so it can assist more first-time buyers, while accounting for a degree of price variation within regions without the additional complexity that may arise from more localised caps.
“Therefore, there are no plans to revise the caps,” he added.
In February the previous version of the Help to Buy scheme, which closed to new applications in December, was extended until 31 May to allow completion of builds and purchases affected by the pandemic.
