The spatial infection kernel contained within spatial disease models is typically of a simple parametric type; for example, exponential or power law. However, often the infection kernel is a proxy for numerous unobserved infection mechanisms; for example, airborne spread, host movement, vector movement and/or direct transmission. Such an amalgamation of mechanisms may be poorly described by a simple parametric spatial function. In this work, we have addressed this problem and developed more flexible non-parametric spatial kernels. These semi-parametric spatial kernels, being linear rather than non-linear as parametric kernels tend to be, can also be used to circumvent computational issues by partitioning the likelihood into a computationally trivial parameter-dependent part and a computational a burdensome parameter-independent part. Here, the proposed models are developed using simulated data and are applied to data from the 2001 UK foot-and-mouth disease epidemic.