Two-dimensional metal halide perovskites (2D MHPs) are promising candidates for ultraviolet (UV) light detection due to their narrow band gap and high stability in the air atmosphere. MHP crystals, with fewer defects and grain boundaries than polycrystalline films, are more suitable for photodetectors and other advanced semiconductor devices. In this paper, aimed to fabricate high-performance UV light detector, a series of high-quality and large-sized 2D perovskite crystals with the composition of (BA)2Pb(ClxBr1-x)4 were prepared and the best UV responsibility was found in the (BA)2Pb(Cl0.1Br0.9)4 crystal. Despite the detector was fabricated by the simple silver brushing method, it exhibits high responsivity of 3.19 mA/W, high detection rate of 3.87 × 1011 Jones, and fast response speed to UV light of 340 nm under the bias of 20 V. Moreover, the detector shows remarkable light sensitivity even under extremely weak UV illumination of 5.4 μW/cm2 and satisfactory stability during a long-duration switching operation. The excellent light response performance of the (BA)2Pb(Cl0.1Br0.9)4 detector was ascribed to the very low dark current (0.84 pA) of the detector, which highly relies on the crystal quality of the light-absorbing perovskites. The relationship between the structural and the compositional characteristics of (BA)2Pb(Cl0.1Br0.9)4 and its light response property was analyzed. This work provides a promising candidate material for sensitive UV detection and high-performance photodetectors.