The figures came at footballer Marcus Rashford called on health professionals to boost awareness of the Healthy Start scheme – which helps pregnant women and struggling families with young children buy basic food supplies.
NHS data shows, in the four weeks to July 18, 1,646 people in the area were receiving vouchers from the scheme, which are worth between £4.25 and £8.50 a week and can be spent on healthy fruit and vegetables, milk or baby formula.
But that represents just 66% of those identified as eligible for the benefit – with the figures showing there may be another 824 families in the area missing out on valuable support.
Nationally 59% of those eligible for the scheme were receiving the support they were entitled to.
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In a letter published in the British Medical Journal, the England and Manchester United star urged family doctors and other health professionals to spread the word about the scheme.
The letter said: "The scheme has proven benefits in improving access to healthy food for pregnant women and children under the age of four but more than 40% of those eligible for the vouchers are still not registered for the scheme.
"No child deserves to be starting life 20 yards behind any other, just because of the circumstances they are born into."
The Food Foundation recently found that 14% of UK families with children had experienced food insecurity in the six months to September 2020.
A spokesman said health care professionals could play "a vital role in actively encouraging awareness in communities".
He added: “There is the issue of stigma. Many young families just feel embarrassed about being perceived to rely on benefits or hand-outs."
A spokesperson for the Department of Health and Social Care said the Government is committed to ensuring every child receives the best possible start in life.
He said an online application form is being developed as an alternative to the current postal system and will be introduced along with a payment card to replace paper vouchers.