Angela Rayner, the shadow education secretary, has spoken about how a Sure Start course taught her as a teenage mother to hug and read to her son, as she promised Labour would give £500m to help reopen many of the 400 centres closed under the Conservatives.

The Labour politician said Sure Start centres, introduced under the last Labour government, had changed her life after she attended parenting lessons at one of the children’s centres, at a time when she felt it was a failure to go to friends and family for help.

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Writing for the Guardian, she said: “I went to my local Sure Start centre, and they put me on a parenting course. I learned things that might seem simple – that it was important to hug and love your child, and read to them. This might seem obvious but it wasn’t to me at the time. If I hadn’t had access to the vital support of my local Sure Start centre, I would never have had the help I – and my son – needed.”

Rayner spoke of being raised on a council estate by her mother, who did everything she could, but could not help with reading and writing because she had never been taught herself.

“As the jargon would have it now, I was not ‘school ready’. And I am no longer ashamed to say that I left school at the age of 16, pregnant and without any qualifications,” she said.

Rayner, who is passionate about services for young children, fought for extra money to be included for Sure Start and other early intervention programmes in the Labour manifesto, rather than the focus being just on students of university age.

The party has not specified how many more children would be helped or how many centres reopened through the early intervention funding, but the £500m-a-year boost would be enough to reopen about 400 scrapped centres and restore services which have reduced facilities.

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The manifesto pledged £5.3bn annually to help families with young children, including the flagship policy of extending 30 hours of free childcare a week to all two- to four-year-olds.

The funding allocation for children’s centres is governed by local authorities, which have been subject to swingeing cuts over the last seven years.

There are about 1,200 fewer designated Sure Start centres than there were in 2010, although some have just limited services and have lost the label rather than being closed or merged.

Rayner, who is a relative newcomer to the shadow cabinet but has been tipped as a possible future leader, said her backing for Sure Start came not just from personal experience but from evidence that early years intervention was the most effective way to improve the outcome for children from the most disadvantaged backgrounds.