The results of astrometric observations of the main Uranian satellites taken with the Faulkes Telescope North are presented. A median filter algorithm was applied to subtract a scattered-light halo caused by Uranus. The Two-Micron All-Sky Survey (2MASS) and USNO-B1.0 were used as reference catalogues. The mean value of the differences between the equatorial coordinates of the satellites determined with 2MASS and USNO-B1.0 is close to 200 mas. A comparison of the observed equatorial coordinates of the satellites and their relative positions with ephemerides based on different combinations of theories of motion of Uranus and its satellites (DE405+GUST86, DE405+GUST06, INPOP+GUST86, INPOP+GUST06) was performed. The satellites' positions obtained with respect to 2MASS are in better agreement with theories. The values of (O-C) of the equatorial coordinates determined with the 2MASS are mainly less than 100 mas. The majority of (O-C) of relative positions are within ±50 mas. The mean values of the standard errors of (O-C) are within 20 to 60 mas.