The presence of differential reddening in the direction of Galactic globular clusters (GCs) has proven to be a serious limitation in the traditional colour-magnitude diagram (CMD) analysis. Here, we estimate local reddening variations in the direction of 56 Galactic GCs. To do that, we use the public catalogues derived as part of the Hubble Space Telescope UV Legacy Survey of Galactic GCs, which include photometry in the F275W, F336W, F438W, F606W, and F814W filters. We corrected photometry for differential reddening and found that for 21 out of 56 GCs the adopted correction procedure significantly improved the CMDs. Moreover, we measure the reddening law in the direction of these clusters, finding that R_V_ exhibits a high level of variability within the Galaxy, ranging from ~2.0 to ~4.0. The updated values of R_V_ have been used to improve the determination of local reddening variations and derive high-resolution reddening maps in the direction of the 21 highly-reddened targets within our sample. To compare the results of the different clusters, we compute the 68^th^ percentile of the differential-reddening distribution, {sigma}{Delta}AF814W. This quantity ranges from 0.003 to 0.030mag and exhibits a significant anticorrelation with the absolute module of the Galactic latitude and a strong correlation with the average reddening in the direction of each cluster. Therefore, highly-reddened GCs located in the proximity of the Galactic plane typically show higher differential-reddening variations across their field of view.