Leith made the call at an event organised by CH&Co-owned school caterer, Principals, called ‘Beyond the Classroom’.
The deal with the independent, day, boarding, nursery and preparatory school for girls, is worth £750,000.
Its catering services unit Food & More serves 32,000 meals a day to students across more than 200 schools as part of FM in Leeds, Barnsley, Redcar, Oxfordshire, Gateshead and Tameside.
Concerns listed among the 1,200 workers surveyed included stress, debt, unpaid overtime and a lack of training.
The contract is worth more than £2.5million over three years.
John Newton, head of PHE’s Health Improvement Directorate, said: “Severely obese children are at risk of developing a number of serious acute and chronic health problems.
Prestfelde School, an independent preparatory boarding school in Shrewsbury, Shropshire, and Highclare School in Birmingham, have both furthered their contracts with the firm by five years.
The Government health body will promote the move to healthier snacks through the launch of its Change4Life campaign.
The provider to 70,000 meals in Birmingham held a series of fundraising events during the year, finishing off with a Christmas jumper day.
Currently families receiving Universal Credit (UC) are eligible, but this will change once UC is rolled out.