Research on robotic manipulation of fragile, compliant objects, such as food items, is gaining traction due to its game-changing potential within the food production and retailing sectors, currently characterized by manually-intensive and highly repetitive tasks. Food products exhibit high levels of frailness, biological variation, and complex 3D shapes and textures. For these reasons, introducing greater levels of robotic automation in the food and agricultural sectors remains an important challenge. This paper addresses this challenge by developing a human-centred, haptic-based, Learning from Demonstration (LfD) policy that enables pre-trained autonomous grasping of food items using an anthropomorphic robotic system. The policy combines data from teleoperation and direct human manipulation of objects, embodying human intent and interaction areas of significance. We evaluated the proposed solution against a recent state-of-the-art LfD policy as well as against two standard impedance controller techniques. Results show that the proposed policy performs significantly better than the other considered techniques, leading to high grasping success rates while guaranteeing the integrity of the food at hand.