We investigate near-ultraviolet (NUV) variability in the Galactic globular cluster (GC) 47 Tucanae (47 Tuc). This work was undertaken within the GC sub-project of the Transient UV Objects project, a programme which aims to find and study transient and strongly variable UV sources. Globular clusters are ideal targets for transient searches because of their high stellar densities and large populations of variable systems. Using all 75 archival observations of 47 Tuc obtained with the UV/optical telescope (UVOT) aboard the Neil Gehrels Swift observatory with the uvm2 filter, we searched for UV variability using a specialised pipeline which utilises difference image analysis. We found four clear transients, hereafter SW1-4, with positions consistent with those of known cataclysmic variables (CVs) or CV candidates identified previously using Hubble Space Telescope observations. All four sources exhibit significant outbursts, likely brightening by several orders of magnitude. Based on the inferred outburst properties and the association with known CVs, we tentatively identify the UV transients as CV-dwarf novae (DNe). Two DNe have been previously observed in 47 Tuc: V2, which has a position consistent with that of SW4; and AKO 9, which was not in outburst during any of the UVOT observations. We thus increase the known number of DNe in 47 Tuc to 5 and the total number of detected DNe in all Galactic GCs combined from 14 to 17. We discuss our results in the context of the apparent scarcity of DNe in GCs. We suggest that the likely cause is observational biases, such as limited sensitivity due to the high background from unresolved stars in the GC and limited angular resolution of the telescopes used. We additionally detected one strongly variable source in 47 Tuc, which could be identified as the known RR Lyrae star HV 810. We found its period to have significantly increased with respect to that measured from data taken in 1988.