The soft nature of metal halide perovskites makes them potentially applicable as flexible X-ray detectors. Here we report a structure of perovskite-filled membranes (PFMs) for highly sensitive, flexible and large-area X-ray detectors. PFMs with areas up to 400 cm² are formed by infiltrating saturated perovskite solution through porous polymer membranes followed by hot lamination. The good connectivity and crystallization of perovskite crystals in the membranes enable a large mobility–lifetime product. The sensitivity of the X-ray detectors under a field of 0.05 V µm⁻¹ reaches 8,696 ± 228 µC Gy_air⁻¹ cm⁻² and shows no degradation after storage for over six months and exposure to a dose of 376.8 Gy_air, equivalent to 1.88 million chest X-ray scans. The flexible PFMs can be bent at radii down to 2 mm without losing performance. The stand-alone detector array is curved and put inside metal pipes for the detection of material defects with imaging quality superior to flat-panel detectors.