The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in mathcal{N} = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of mathcal{N} = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the mathcal{N} = 4 SYM case, as we speculate in the last part of the article.