Worcester-based VMB has taken on an additional 25 staff to handle the work, which involves printing millions of items over the three-year span of the deal.
VMB business director Brian Taylor cited his company's recent multimillion-pound investment in new equipment as key to the contract win.
However, the move has come as a blow to the encumbent contract holder. Derbyshire-based Amcor Flexibles is in consultation to halve the workforce at its Ilkeston site resulting in the possible loss of 75 jobs.
Amcor general manager Rob Baxter said that the loss of the contract would have "an immediate impact... and means we have no option but to take action to reduce costs", but would not comment further while consultations were ongoing.
"We will be exploring all possibilities to preserve jobs, either at the plant or elsewhere within Amcor, and of course we'll be looking to agree appropriate conditions should the redundancies go ahead," he said.
A local media report claimed that production of bread bags, which had previously been manufactured at the Ilkeston site, would now be moved to China because of cheaper labour costs. However, Allied could not be reached for comment at the time of publishing.