Blind system identification is aimed at finding parameters of a system model when the input is inaccessible. In this paper, we propose a blind system identification method that delivers a single-input single-output, continuous-time model in a nonparametric kernel form. We take advantage of the representer theorem to form a joint maximum a posteriori estimator of the input and system impulse response. The identified system model and input are optimised in sequence to overcome the blind problem with generalised cross validation used to select appropriate hyperparameters given some fixed input sequence. We demonstrate via Monte Carlo simulations the accuracy of the method in terms of estimating the input.