The WFCAM Transit Survey (WTS) is a near-infrared transit survey running on the United Kingdom Infrared Telescope (UKIRT). We conduct Monte Carlo transit injection and detection simulations for short period (<10 day) Jupiter-sized planets to characterize the sensitivity of the survey. We investigate the recovery rate as a function of period and magnitude in 2 hypothetical star-planet cases: M0-2 + hot Jupiter, M2-4 + hot Jupiter. We find that the WTS lightcurves are very sensitive to the presence of Jupiter-sized short-period transiting planets around M dwarfs. The non-detection of a hot-Jupiter around an M dwarf by the WFCAM Transit Survey allows us to place a firm upper limit of 1.9 per cent (at 95 per cent confidence) on the planet occurrence rate.