Composite materials are widely used in industry due to their light weight and specific performance. Currently, composite manufacturing mainly relies on manual labour and individual skills, especially in transport and lay-up processes, which are time consuming and prone to errors. As part of a preliminary investigation into the feasibility of deploying autonomous robotics for composite manufacturing, this paper presents a case study that investigates a cooperative mobile robot and manipulator system (Co-MRMS) for material transport and composite lay-up, which mainly comprises a mobile robot, a fixed-base manipulator and a machine vision sub-system. In the proposed system, marker-based and Fourier transform-based machine vision approaches are used to achieve high accuracy capability in localisation and fibre orientation detection respectively. Moreover, a particle-based approach is adopted to model material deformation during manipulation within robotic simulations. As a case study, a vacuum suction-based end-effector model is developed to deal with sagging effects and to quickly evaluate different gripper designs, comprising of an array of multiple suction cups. Comprehensive simulations and physical experiments, conducted with a 6-DOF serial manipulator and a two-wheeled differential drive mobile robot, demonstrate the efficient interaction and high performance of the Co-MRMS for autonomous material transportation, material localisation, fibre orientation detection and grasping of deformable material. Additionally, the experimental results verify that the presented machine vision approach achieves high accuracy in localisation (the root mean square error is 4.04 mm) and fibre orientation detection (the root mean square error is 1.84∘) and enables dealing with uncertainties such as the shape and size of fibre plies.