Low-cost uncrewed aerial vehicles (UAVs) are replacing manned aircraft for airborne radiation mapping applications such as nuclear accident response scenarios or surveying ore deposits and mine sites because of their cost-effectiveness and ability to conduct surveys at lower altitude compared to manned counterparts. Both multi-rotor UAVs and fixed-wing UAVs are well established technologies for aerial radiation mapping applications, however, both also have drawbacks: multi-rotor UAVs are very limited in flight time and range, and fixed-wing UAVs usually require facilities for take-off and landing. A compromise solution is introduced in this work, using a fixed-wing vertical take-off and landing (VTOL) UAV that combines the flexibility of a multi-rotor UAV with the range and flight time of a fixed-wing UAV. The first implementation of a VTOL with radiation mapping capabilities is presented, based on a commercial WingtraOne UAV augmented with CsI scintillator and CZT semiconductor gamma spectrometers. The radiation mapping capabilities of the prototype are demonstrated in a case study, mapping the distribution of radionuclides around the South Terras legacy uranium mine in the south of England, United Kingdom, and the results are compared with previous studies using multi-rotor and manned aircraft to survey the same area.