High fracture toughness at cryogenic temperature and radiation hardness can be conflicting requirements for the resins for the impregnation of superconducting magnet coils. The fracture toughness of different epoxy-resin systems at room temperature (RT) and at 77 K was measured, and their toughness was compared with that determined for a polyurethane, polycarbonate (PC) and poly(methyl methacrylate) (PMMA). Among the epoxy resins tested in this study, the MY750 system has the highest 77 K fracture toughness of KIC = 4.6 MPa√m, which is comparable to the KIC of PMMA, which also exhibits linear elastic behaviour and unstable crack propagation. The polyurethane system tested has a much higher 77 K toughness than the epoxy resins, approaching the toughness of PC, which is known as one of the toughest polymer materials. CTD101K is the least performing in terms of fracture toughness. Despite this, it is used for the impregnation of large Nb3Sn coils for its good processing capabilities and relatively high radiation resistance. In this study, the fracture toughness of CTD101K was improved by adding the polyglycol flexibiliser Araldite DY040 as a fourth component. The different epoxy-resin systems were exposed to proton and gamma doses up to 38 MGy, and it was found that adding the DY040 flexibiliser to the CTD101K system did not significantly change the irradiation-induced ageing behaviour. The viscosity evolution of the uncured resin mix is not significantly changed when adding the DY040 flexibiliser, and at the processing temperature of 60 °C, the viscosity remains below 200 cP for more than 24 h. Therefore, the new resin referred to as POLAB Mix is now used for the impregnation of superconducting magnet coils.