The response speed of the reported Cs2AgBiBr6-based photodetectors exhibits a wide variation ranging from microseconds to nanoseconds, while the reason is still unclear. Apart from the conventional approaches such as reducing effective area, new regulating approaches for response speed improvement have rarely been reported. On the other hand, it is generally believed that ultraviolet (UV) light has negative impact on perovskite devices resulting in performance degradation. In this work, we demonstrated that the response speed of the photodetector with FTO/Cs2AgBiBr6/Au structure can be effectively regulated by utilizing UV light-soaking effect without reducing the device area. Particularly, the decay time is efficiently modulated from 30.1 mu s to 340 ns. In addition, the -3 dB bandwidth of the device is extended from 5 to 20 kHz. It is worth mentioning that the light current is remarkably boosted by 15 times instead of any attenuation. Furthermore, we prove the universality of UV soaking treatment on Cs2AgBiBr6-based photodetectors with other all-inorganic structures, i.e., FTO/TiO2/Cs2AgBiBr6/Au, FTO/Cs2AgBiBr6/TiO2/Au and FTO/TiO2/Cs2AgBiBr6/CuSCN/Au. Our results demonstrate a new method to improve the response speed and light current of Cs2AgBiBr6-based perovskite all-inorganic photodetectors.