We describe a laser–plasma platform for photon–photon collision experiments to measure fundamental quantum electrodynamic processes. As an example we describe using this platform to attempt to observe the linear Breit–Wheeler process. The platform has been developed using the Gemini laser facility at the Rutherford Appleton Laboratory. A laser Wakefield accelerator and a bremsstrahlung convertor are used to generate a collimated beam of photons with energies of hundreds of MeV, that collide with keV x-ray photons generated by a laser heated plasma target. To detect the pairs generated by the photon–photon collisions, a magnetic transport system has been developed which directs the pairs onto scintillation-based and hybrid silicon pixel single particle detectors (SPDs). We present commissioning results from an experimental campaign using this laser–plasma platform for photon–photon physics, demonstrating successful generation of both photon sources, characterisation of the magnetic transport system and calibration of the SPDs, and discuss the feasibility of this platform for the observation of the Breit–Wheeler process. The design of the platform will also serve as the basis for the investigation of strong-field quantum electrodynamic processes such as the nonlinear Breit–Wheeler and the Trident process, or eventually, photon–photon scattering.