Ba1−x K x Fe2As2 superconductors have strong potential for magnet applications through their very high upper critical field, relatively high superconducting transition temperature and manufacturability through the powder-in-tube (PIT) route. However, the critical current density in PIT tapes is still low compared to the incumbent technologies, so a greater understanding of the limiting factors is required. We have measured the in-field critical currents (I c) of stainless steel and silver double-sheathed monofilament Ba0.6K0.4Fe2As2 superconductor tapes at elevated temperatures from 15 K to 35 K. At 20 K, the critical current density is up to 140 kA cm−2 in low (optimal) field and 22 kA cm−2 in 8 T. In the low-field region we observe an anomalous and sharp suppression of I c centred at the zero field. This feature is non-hysteretic for lower temperatures and perpendicular fields, but becomes hysteretic for higher temperatures in perpendicular fields and for all temperatures in parallel fields. The low-field suppression is also reflected in the n-values which can otherwise be very high, in excess of 100 in the optimal field. Magnetic-field hysteresis of I c is generally attributed to flux exclusion/flux trapping in granular superconductors and this is likely to be the case also in the present conductors. The low-field I c anomaly also likely has its origin in planar granularity, while magnetic phases in grains or grain boundaries may also play a role.