The non-local symmetries for the generalized Broer–Kaup (BK) system are obtained with the truncated Painlevé expansion method. The non-local symmetries can be localized to the Lie point symmetries for the extended system by introducing auxiliary dependent variables. The finite symmetry transformations related to the non-local symmetries are computed. The consistent Riccati expansion and consistent tanh expansion integrability of the generalised BK system are proved, and the single soliton, two-resonant soliton and soliton–cnoidal wave interaction solutions are derived.