Major concessions have put the government in a “better position” to pass welfare reforms, the health secretary said, as he admitted Labour’s leadership mishandled the rollout of its flagship bill.

Wes Streeting said Labour MPs had raised “substantial” concerns about planned welfare cuts, and the government strengthen its plans as a result.

Last week, the prime minister was forced into a dramatic U-turn to avoid a House of Commons defeat after more than 120 Labour backbenchers threatened to vote down his plans.

“We are in a much better position this week than last week,” Streeting told the BBC’s Sunday with Laura Kuenssberg, and said the government has to “learn” from narrowly avoiding rebellion.

Streeting said the government had shifted “not just the package but also the approach” following criticism that the original proposals risked undermining support for disabled people.

Last week, the government faced a growing rebellion from Labour MPs who warned the planned welfare cuts, aimed at saving £5bn annually, were rushed and would hurt vulnerable people.

The government’s initial plans, aimed at bringing down the welfare bill, would have made it harder for people to claim personal independence payment (Pip), a benefit paid to 3.7 million people with long-term physical or mental health conditions.

The backlash culminated in a late-night announcement of major concessions to the rebel MPs – including limiting Pip cuts to only new claimants.

It reversed its plans to freeze the health-related component of universal credit, and the payment will now rise in line with inflation for existing recipients.

The government also announced plans for a review of the Pip assessment to be led by disabilities minister Sir Stephen Timms and “co-produced” with disabled people.

Louise Haigh, one of the leading rebel MPs, told the BBC she now planned to support the bill following the government’s changes.

Speaking on the same programme, Haigh, the Labour MP for Sheffield Heeley, said her fellow rebel MPs are “really pleased that the government has now listened to those concerns and they’ve made a significant number of concessions”.

Subject to seeing the final detail of the changes, she said: “I will be supporting the government on Tuesday in recognition that they have made significant progress and that they have protected the incomes of nearly 400,000 disabled people across the country.”

Rebels have told the BBC their colleagues are happy with the concessions – meaning the Universal Credit and Personal Independence Payment Bill will not be blocked in a vote on Tuesday, although some Labour MPs have said they will still vote against the proposals.

The episode has raised questions about the prime minister’s political strategy and ability to manage internal dissent.

Over the weekend, Sir Keir Starmer gave an interview with the Sunday Times to defend his handling of the row, pointing out he was abroad attending a Nato conference during the height of the rebellion.

Shadow work and pensions secretary Helen Whately accused Labour of “delaying or cancelling” Conservative plans to fix welfare, leading to a “wasted” year.

“We find ourselves one year later in a worse situation than we were when they came into power,” she told the BBC.

She pointed to a report by the Centre for Social Justice, which argued cutting mental health benefits for all but the worst cases would save of £7.4bn per year by 2030.

The savings could be used to fund 1.5 million additional therapy courses for people with mental-health conditions, the report argued.

On Sunday, Streeting defended the government’s intentions, saying the reforms were necessary to ensure the long-term sustainability of the welfare system.

“No one will thank us if we carry on with the status quo,” he said.

“Unless you reform this system, I genuinely fear it will not be there for anyone in the future.”

Streeting did not rule out future changes to welfare following the Timms review.

Asked if there could be further concessions on personal independence payments, he said “we have got to listen”.

His comments came after Sir Keir claimed “fixing” the welfare system is a “moral imperative”.

The prime minister told the Welsh Labour Party conference in Llandudno on Saturday that the government would not take away the welfare “safety net that vulnerable people rely on”.

But he said he could not let benefits “become a snare for those who can and want to work”.