Regularisation is a common method in iterative solutions for imaging inverse problems. The majority of algorithms evaluate the proximal operator of the regulariser in every iteration, leading to a significant computational overhead, as such evaluations can be costly. In this context, we investigate skipping the regulariser to reduce the frequency of proximal operator computations. This approach shows a reduction in computational time without compromising convergence or image quality. Here we study for the first time the efficacy of regularisation skipping on a variety of imaging inverse problems. We build upon the ProxSkip algorithm and we also propose a novel skip-version of the PDHG algorithm. Extensive numerical results highlight the potential of these methods to accelerate computations while maintaining high-quality reconstructions.