Critical UV applications such as disinfections and dermatological treatments call for accurate UV spectral irradiation measurements. Single monochromators and spectrographs are not able to provide satisfying accuracy due to poor stray light rejection. The main drawbacks of a double monochromator scanning system are the need for motion synchronization, the inconvenience in performing field measurements and the time-consuming scanning approach. In this paper, a combination of a monochromator with a large bandpass and a spectrograph is proposed, which allows for accurate UV spectral irradiance measurements with short measurement times of less than 1 s, and yet with acceptable stray light rejection. Stray light levels are determined for both monochromatic and heterochromatic primary radiation using slit functions and cut-off filters. These experiments revealed a considerable UV stray light response reduction for the monochromator-spectrograph combination compared to single spectrograph instruments. The stray light performance in the 250-400 nm range matches with results obtained with double monochromator instruments. With this setup, the quality of a double dispersing instrument is combined with the quick data acquisition of a spectrograph.