Ministers have come under pressure to increase their commitment to Sure Start early years centres as a tribute to their political architect, Tessa Jowell, who died of brain cancer at the weekend.

Labour MPs lined up to urge the government to invest in the flagship programme, which was established by the Labour government in 1998 to help give disadvantaged children the best possible start in life.

The former shadow education secretary Lucy Powell urged Damian Hinds, the education secretary, to “look again” at the scheme, which has transformed hundreds of thousands of lives across the country.

More than 3,000 centres were opened during Labour’s years in power, but hundreds were closed after the coalition government came to power in 2010, a move that Jowell described as heartbreaking.

The Labour MP Lisa Nandy, who was Jowell’s parliamentary aide during her time as shadow Olympics minister, told the Guardian: “Sure Start was one of Tessa’s greatest achievements. She knew how important family life was to her and how important strong families in particular are to disadvantaged children.

“She was desperate when the programme was scaled back to such a great extent across the country. She had hoped there had been a cross-party consensus behind it that would protect it.

“In the last few days the number of people who have spoken up to talk about what it means to them is one of the things she would’ve been proudest of, and demonstrates why Sure Start matters so much and ought to be reinstated.”

Angela Rayner, the shadow education secretary, hailed Jowell’s role in setting up the programme. She told MPs: “When I was a young mum, it was the Sure Start centre that really helped me and my son. And for all that’s said and done in this chamber, that is the best that any honourable member can hope to have achieved.”

Yvette Cooper described Jowell, a former cabinet minister, as the “mother of Sure Start”. Emily Thornberry, the shadow foreign secretary, said: “The greatest tribute the government could pay to her would be to begin again the proper funding of her most important achievement: Sure Start.”

Hinds told MPs he shared the view on “the fundamental importance of the early years” but declined to make any promises, speaking instead about the importance of home life and nursery care, as well as early years centres, in boosting life chances.