We consider two rubidium atoms, prepared in the same S or P Rydberg states, near an optical nanofibre, and we determine their van der Waals interaction potential as a function of their separation along the nanofibre axis, their distance to the nanofibre axis, and their relative azimuthal angle. We compare results obtained through direct diagonalisation of the Hamiltonian (including quadrupolar interaction terms) with second-order perturbation calculations, and we identify which couplings mainly contribute to the potential in the presence of the nanofibre and in free-space. We relate the appearance of new allowed couplings to the broken rotation symmetry around the interatomic axis due to the presence of the fibre. These couplings induce novel features and cause a reshaping of the interaction anisotropy and formation of an interaction potential well for P states near the nanofibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.