The chancellor, Rishi Sunak, has been criticised by MPs for “drawing a line” under concerns that more than a million people have missed out on the government’s emergency coronavirus support schemes.

The influential Treasury committee issued its rebuke as it published the government’s response to recommendations put forward by MPs to help make up for a gap in support. The original report, released last month, found more than a million people who had recently switched jobs, were newly self-employed, directors of limited companies, or freelancing were effectively locked out of financial aid programmes.

The cross-party committee’s recommendations included giving short-term contractors and freelancers access to financial support, making an extra effort to calculate the income of people who pay themselves via company dividends, and extending the cut-off date by which staff had to be employed to qualify for the furlough scheme.

However, the chancellor did not offer to alter any of the programmes in his response and said that while he “carefully considered” some of the recommendations, there were “practical” reasons for maintaining strict eligibility criteria that in many cases would help block fraud.

Sunak also defended the government’s track record in providing support, saying it had been “comprehensive in the economic response it has rolled out”.

But Mel Stride, the Conservative chair of the committee, said the response showed the chancellor had “effectively drawn a line under helping the million-plus people who have been excluded from support for four months”.

“Despite stating that he will not pick winners and losers when it comes to sectors and businesses that need support, the chancellor has done this when it comes to households and individuals,” Stride said, adding that the committee was still not convinced that the government could not have helped more people.

“The chancellor initially told those at risk of losing their livelihoods that they would not be forgotten. While the government is clear that it is moving on to the next phase of its recovery plan, it cannot just turn its back on those who are suffering.”

Stride urged the government to rethink its position.

The comments come as Sunak prepares to scale back the multibillion-pound emergency financial support programme in the coming months, as the government tries to move away from the initial crisis phase of the pandemic.

From the start of next month, the coronavirus job retention scheme (CJRS) – launched in March to pay 80% of furloughed workers’ wages – will be cut back. Despite warnings from experts over rapidly rising levels of unemployment, it will be closed by the end of October.

As many as 9.5m jobs have been furloughed on the scheme at 1.2m companies, at a cost to the exchequer of £29.8bn so far. Sunak used his summer statement to offer £1,000 bonuses to employers that retain furloughed staff, although experts have warned the scheme could have a limited impact.

In his response to the Treasury committee’s report, Sunak defended his efforts, saying that people who have struggled to access the furlough scheme or self-employment income support scheme “could look for support from the many measures we have launched to make sure people get help at this time”.

He said: “The government has ensured people who needed it received help with their utility bills and had access to mortgage and consumer credit holidays. To make sure we reached the most vulnerable, the government gave local councils an additional £500m to provide all recipients of working-age local council tax support.”