In this study, the effects of adding nanofillers to an epoxy resin (EP) used as a matrix in glass fibre-reinforced plastic (GFRP) composites have been investigated. Both 1D and 2D nanofillers were used, specifically (1) carbon nanotubes (CNTs), (2) few-layer graphene nanoplatelets (GNPs), as well as hybrid combinations of (3) CNTs and boron nitride nanosheets, and (4) GNPs and boron nitride nanotubes (BNNTs). Tensile tests have shown improvements in the transverse stiffness normal to the fibre direction of up to about 25% for the GFRPs using the ‘EP + CNT’ and the ‘EP + BNNT + GNP’ matrices, compared to the composites with the unmodified epoxy (‘EP’). Mode I and mode II fracture toughness tests were conducted using double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively. In the quasi-static mode I tests, the values of the initiation interlaminar fracture toughness, GCIC, of the GFRP composites showed that the transfer of matrix toughness to the corresponding GFRP composite is greatest for the GFRP composite with the GNPs in the matrix. Here, a coefficient of toughness transfer (CTT), defined as the ratio of mode I initiation interlaminar toughness for the composite to the bulk polymer matrix toughness, of 0.68 was recorded. The highest absolute values of the mode I interlaminar fracture toughness at crack initiation were achieved for the GFRP composites with the epoxy matrix modified with the hybrid combinations of nanofillers. The highest value of the CTT during steady-state crack propagation was ~ 2 for all the different types of GFRPs. Fractographic analysis of the composite surfaces from the DCB and ENF specimens showed that failure was by a combination of cohesive (through the matrix) and interfacial (along the fibre/matrix interface) modes, depending on the type of nanofillers used.