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Outbursts from cataclysmic variables, such as dwarf novae (DNe), are prevalent throughout the galaxy and are known to emit strongly in the ultraviolet (UV). However, the UV emission of DNe has not been studied extensively compared with the optical. Characterising in detail the physical processes responsible for DN outburst behaviour requires further UV data. Here we report, as part of our recently launched Transient UV Objects Project (TUVO), the discovery of TUVO-21acq, a new transient which we detected in the UV using data from the Ultraviolet Optical Telescope aboard Swift. We detected two separate outbursts and used the UV data to constrain source properties, focusing on the amplitudes and timescales of the outbursts. During the first outburst the source increased in brightness by >4.1, >2.4, and >3.5 magnitudes and during the second outburst by >4.4, >3.4, and >3.6 magnitudes in the UVW1, UVM2, and UVW2 bands, respectively. The outburst durations were in the range 6-21 days and 11-46 days, and the recurrence time is <316 days. We additionally obtained an optical spectrum during quiescence with SALT. The spectrum exhibited hydrogen Balmer series and helium emission lines, and a flat overall spectral shape. We confirm the nature of the source as an accreting white dwarf which underwent DN outburst based on photometric and spectroscopic properties. This study serves as a proof-of-concept for the TUVO project strategy, demonstrating its capability of discovering and classifying new, interesting UV transients. We discuss the implications of our findings for our understanding of the physics underlying DN outbursts, in particular with respect to the UV emission. We examine the need for simultaneous UV and optical observations during the onset of DN outbursts in order to help answer remaining questions, for example in the characteristics and implications of the UV delay.