Generalised CP transformations are the only known framework which allows to predict Majorana phases in a flavour model purely from symmetry. For the first time generalised CP transformations are investigated for an infinite series of finite groups, $\Delta(6n^2)=(Z_n\times Z_n)\rtimes S_3$. In direct models the mixing angles and Dirac CP phase are solely predicted from symmetry. $\Delta(6n^2)$ flavour symmetry provides many examples of viable predictions for mixing angles. For all groups the mixing matrix has a trimaximal middle column and the Dirac CP phase is 0 or $\pi$. The Majorana phases are predicted from residual flavour and CP symmetries where $\alpha_{21}$ can take several discrete values for each $n$ and the Majorana phase $\alpha_{31}$ is a multiple of $\pi$. We discuss constraints on the groups and CP transformations from measurements of the neutrino mixing angles and from neutrinoless double-beta decay and find that predictions for mixing angles and all phases are accessible to experiments in the near future.