Allum joined First Milk from McDonald's in 2009, initially as group operations director and latterly she has been executive director for cheese.
First Milk's chairman, Bill Mustoe, commented: "Over the last few months I have covered the chairman and chief executive roles, which has enabled me to get a strong understanding of the business.
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Hide Ad"However, the time is now right for me to concentrate on strategy and First Milk's position in the marketplace.
"Therefore I will hand over chief executive responsibilities to Kate, who has demonstrated a clear ability to drive change in First Milk, while motivating people to deliver challenging goals.
"Achieving sustained progress for First Milk involves putting in place a number of changes that will help us to increase the returns we can pay to members. This appointment is part of these changes."