We report the discovery of WTS-1b, the first extrasolar planet found by the WFCAM Transit Survey, which began observations at the 3.8-m United Kingdom Infrared Telescope (UKIRT) in 2007 August. Light curves comprising almost 1200 epochs with a photometric precision of better than 1 per cent to J ˜ 16 were constructed for ˜60 000 stars and searched for periodic transit signals. For one of the most promising transiting candidates, high-resolution spectra taken at the Hobby-Eberly Telescope (HET) allowed us to estimate the spectroscopic parameters of the host star, a late-F main-sequence dwarf (V = 16.13) with possibly slightly subsolar metallicity, and to measure its radial velocity variations. The combined analysis of the light curves and spectroscopic data resulted in an orbital period of the substellar companion of 3.35 d, a planetary mass of 4.01 ± 0.35 MJ and a planetary radius of 1.49-0.18+0.16 RJ. WTS-1b has one of the largest radius anomalies among the known hot Jupiters in the mass range 3-5 MJ. The high irradiation from the host star ranks the planet in the pM class. Based on observations collected at the 3.8-m United Kingdom Infrared Telescope (Hawaii, USA), the Hobby-Eberly Telescope (Texas, USA), the 2.5-m Isaac Newton Telescope (La Palma, Spain), the William Herschel Telescope (La Palma, Spain), the German-Spanish Astronomical Centre (Calar Alto, Spain), the Kitt Peak National Observatory (Arizona, USA) and the Hertfordshire's Bayfordbury Observatory.