The WFCAM Transit Survey (WTS) is a near-infrared transit survey running on the United Kingdom Infrared Telescope (UKIRT), designed to discover planets around M dwarfs. The WTS acts as a poor-seeing backup programme for the telescope, and represents the first dedicated wide-field near-infrared transit survey. Observations began in 2007 gathering J-band photometric observations in four (seasonal) fields. In this paper, we present an analysis of the first of the WTS fields, covering an area of 1.6 square degrees. We describe the observing strategy of the WTS and the processing of the data to generate light curves. We describe the basic properties of our photometric data, and measure our sensitivity based on 950 observations. We show that the photometry reaches a precision of ˜4 mmag for the brightest unsaturated stars in light curves spanning almost 3 yr. Optical (SDSS griz) and near-infrared (UKIRT ZYJHK) photometry is used to classify the target sample of 4600 M dwarfs with J magnitudes in the range 11-17. Most have spectral types in the range M0-M2. We conduct Monte Carlo transit injection and detection simulations for short-period (<10 d) Jupiter- and Neptune-sized planets to characterize the sensitivity of the survey. We investigate the recovery rate as a function of period and magnitude for four hypothetical star-planet cases: M0-2+Jupiter, M2-4+Jupiter, M0-2+Neptune and M2-4+Neptune. We find that the WTS light curves are very sensitive to the presence of Jupiter-sized short-period transiting planets around M dwarfs. Hot Neptunes produce a much weaker signal and suffer a correspondingly smaller recovery fraction. Neptunes can only be reliably recovered with the correct period around the rather small sample (˜100) of the latest M dwarfs (M4-M9) in the WTS. The non-detection of a hot Jupiter around an M dwarf by the WTS allows us to place an upper limit of 1.7-2.0 per cent (at 95 per cent confidence) on the planet occurrence rate.