Some council services, including Sure Start sessions and adult day centres, have also been closed.
All 36 Sure Start centres are Ofsted-registered and provide childcare, education, health and family support.
Sure Start and the free nursery places have had more impact on the poorest children.
The delegation included a local NHS worker, Sure Start worker, fire service representatives and local government representatives.
His proposal to re-evaluate the effectiveness of Sure Start will be uncomfortable for his Liberal Democrat coalition partners.
In December, Portsmouth council's first set of spending cuts included closing children's Sure Start centres and public toilets.
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Unite have promised a "grassroots campaign" to defend local services such as libraries, Sure Start centres and swimming pools.
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We're focusing Sure Start at the poorest families, with 4, 200 extra health visitors.
Public Health Minister Tessa Jowell also takes charge of the Sure Start Programme and women's issues in the Commons.
Early studies suggest that the quality of Sure Start child care is variable.
But, in separate exchanges, he challenged Mr Cameron to "get a grip" over the funding of Sure Start children's centres.
The announcement includes a promise that core school funding, Sure Start and 16-19 funding would be protected for one year.
The threat will increase, they argue, as the government expands its Sure Start programme, aimed at the country's poorest families.
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Programmes such as Sure Start, launched in 1999 to provide parenting advice and facilities in Britain's poorest boroughs, have proved popular.
Mr Boles is the parliamentary private secretary to Schools Minister Nick Gibb, in the education department which has oversight over Sure Start.
Anne Longfield, chief executive of 4Children, which runs Sure Start children's centres, said it undermined the government's commitment to children and families.
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They are also concerned that poor families with young children will be adversely affected as councils facing budget cuts reduce Sure Start services.
This will help all children get a sure start in life, help parents balance their work and family life and support local communities.
The minister was announcing the creation of "Sure Start Children's Centres", which will provide assistance in several different overlapping fields - including education, health, childcare and employment.
The Sure Start programme is intended to provide integrated support for families in deprived areas, and the Children's Centres are intended as the beginning of a national network.
"No one can volunteer at a library or a Sure Start centre if it's being closed down, " he said in an article for The Independent on Sunday.
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And he suggested that initiatives such as Sure Start should be engaged in "outreach" work to give advice about improving home safety, such as fitting smoke alarms and stair-gates.
The government also removed the protection from the Sure Start budget, leaving them potentially at risk as councils seek to make up losses to their central government grants overall.
The lack of evidence means that belief in the success or failure of Sure Start is as much a question of ideological preferences as it is of social science.
The funding is currently part of the Early Intervention Grant paid by central government to local authorities in England to support early years and family intervention programmes, including Sure Start Children's Centres.
"We have named the best joined-up early years services as Sure Start Children's Centres and they will act as a model to transform future provision for young children and families, " said Ms Hodge.
Conservative MP Nick Boles is also urging a significant further scaling back of tax credits and housing benefit, and a re-examination of the "lazy sentimentalism" of the Sure Start programme of children's centres.
The idea that you've got to have your Sure Start centre and your library and everything all in separate places because otherwise there won't be places for people to volunteer is simply absurd.
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Shadow children's minister Sharon Hodgson criticised the coalition's policy towards Sure Start - a children's centre network established by Labour in the late 1990s to give more deprived children a better chance in life.
Some of the 3, 600 Sure Start children's centres are being cut because the grant that funds them was cut by 11% in last year's emergency budget, and again in the comprehensive spending review by almost the same percentage.
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