Daresbury Laboratory is currently building an Energy Recovery Linac Prototype (ERLP) that serves as a testbed for the study of beam dynamics and accelerator technology important for the design and construction of the proposed 4th Generation Light Source (4GLS) project. Two major objectives for the ERLP are the operation of an oscillator infra-red FEL and demonstration of energy recovery from an electron bunch with an energy spread induced by the FEL. In this paper we present start-to-end simulations including the FEL of the ERLP. The beam dynamics in the high-brightness injector, which consists of a DC photocathode gun and a super-conducting booster, have been modelled using the particle tracking code ASTRA. After the main linac, in which the particles are accelerated to 35 MeV, particles have been tracked with the code ELEGANT. The 3D code GENESIS was used to model the FEL interaction with the electron beam. Different modes of operation and their impact on the design of the ERLP are discussed.