A new microwave photonic signal processing structure for realising in-phase/quadrature (I/Q) mixing is presented. It is based on a dual-drive Mach Zehnder modulator (DDMZM) and an optical phase modulator inside a Sagnac loop interferometer. Two output IF signals with a quadrature phase difference are obtained by using two photodetectors to detect the upper and lower sidebands of the optical signal at the Sagnac loop output. A quadrature phase difference in the two IF signals is realised by biasing the DDMZM at the quadrature point. This has the advantage of very little quadrature phase errors as a standard modulator bias controller can accurately lock the DDMZM bias point. The optical phase modulator driven by an RF signal can be placed in a remote location for antenna remoting. Theoretical analysis and simulation show using the proposed I/Q mixer for image rejection can overcome the modulation index dependent image rejection ratio problem in the reported I/Q mixers based on a cascaded modulator structure. The Sagnac loop based I/Q mixer is experimentally verified with results show only ±1° quadrature phase error and more than 50 dB image rejection ratio over the operating frequency range of 6 to 20 GHz.