We present a computational framework to explore the effect of microstructure and constituent properties upon the fracture toughness of fibre-reinforced polymer composites. To capture microscopic matrix cracking and fibre-matrix debonding, the framework couples the phase field fracture method and a cohesive zone model in the context of the finite element method. Virtual single-notched three point bending tests are conducted. The actual microstructure of the composite is simulated by an embedded cell in the fracture process zone, while the remaining area is homogenised to be an anisotropic elastic solid. A detailed comparison of the predicted results with experimental observations reveals that it is possible to accurately capture the crack path, interface debonding and load versus displacement response. The sensitivity of the crack growth resistance curve (R-curve) to the matrix fracture toughness and the fibre-matrix interface properties is determined. The influence of porosity upon the R-curve of fibre-reinforced composites is also explored, revealing a stabler response with increasing void volume fraction. These results shed light into microscopic fracture mechanisms and set the basis for efficient design of high fracture toughness composites.