This paper presents the results of a Monte Carlo study of the time resolution of a scintillating fibre detector and analyses its dependence on the various aspects of detector construction. The estimations of the theoretical time resolutions for detectors with different numbers of fibre layers and different types of acrylic-based fibre coatings are presented. The method is suggested to decrease the rate counting effects encountered in high rate applications. It has been observed that for dual cladding fibres with a fluorinated polymer used for the outer cladding, the most significant factor contributing to the time resolution is the number of fibre layers, with the fibre coating being the marginal one. Another observation shows that the introduction of a gap between the fibre and the photomultiplier glass window allows the reduction of the number of photoelectrons by 25% with only a slight decrease in the time resolution, which may be helpful in decreasing the pulse pile-up effects and the photomultiplier gain, commonly observed under high rate conditions.