Motivated by the recent work of Kakkar, Shrivas and Singh on interpolative Hardy–Rogers–Meir–Keeler type contractions in complete metric spaces, we investigate their cyclic counterpart. We introduce a class of mappings called interpolative Hardy–Rogers–Meir–Keeler type cyclic contractions. For this class of cyclic mappings, we establish a fixed point result in complete metric spaces and derive conditions ensuring existence and uniqueness of fixed points. An application to a class of nonlinear Hammerstein integral equations is also given, together with an illustrative example.