We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hp elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac electrophysiology where sharp gradients in the solution benefit from the high-order discretisation, while the compu- tational cost of anatomically-realistic models can be reduced through the surface representation. We describe and validate our discretisation and provide a demonstration of its application to modeling electrochemical propagation across a human left atrium.