The Ministry of Defence (MOD) does not collect or hold information on the use of food banks by either current military or civilian personnel, or by Armed Forces veterans. Any decision to use a food bank is a private and personal matter for the individual concerned.
To support those leaving Service, including those medically discharged, the MOD provides points of contact for veterans who are facing challenges when transitioning back into civilian life. The Defence Holistic Transition Policy was introduced to support a whole range of life-changing issues, which affect both the Service Person and their immediate family upon leaving the Services. This could include help with life's basic needs such as registering with a doctor or a dentist, or it could be much more intensive for those with complex needs (including housing, budgeting, debt, wellbeing, and children's education).
Defence Transition Services (DTS), which is part of the MOD's Veterans UK, was established at the same time as the transition policy to provide information and support for those service leavers and their families who are most likely to face challenges as they leave the Armed Forces and adjust to civilian life: https://www.gov.uk/guidance/help-and-support-for-service-leavers-and-their-families. DTS will be there as a safety net for up to two years after leaving Service, and self-referrals can be made through the gov.uk website or by contacting Veterans UK direct.
In addition, the Veterans Welfare Service, part of Veterans UK, provides telephone and face to face assistance from four UK welfare centres to veterans in need of support: https://www.gov.uk/guidance/veterans-welfare-service