Superluminous supernovae (SLSNe) have been detected to z similar to 4 and can be detected to z greater than or similar to 15 using current and upcoming facilities. SLSNe are extremely UV luminous, and hence objects at z greater than or similar to 7 are detected exclusively via their rest-frame UV using optical and infrared facilities. SLSNe have great utility in multiple areas of stellar and galactic evolution. Here, we explore the potential use of SLSNe type-I (SLSNe-I) as high-redshift cosmological distance indicators in their rest-frame UV. Using an SLSN-I sample in the redshift range 1 less than or similar to z less than or similar to 3, we investigate correlations between the peak absolute magnitude in a synthetic UV filter centred at 250 nm and the rise time, colour, and decline rate of SLSNe-I light curves. We observe a linear correlation between M-0(250) and the rise time with an intrinsic scatter of 0.29. Interestingly, this correlation is further tightened (sigma(int) approximate to 0.2) by eliminating those SLSNe that show a pre-peak bump in their light curve. This result hints at the possibility that 'bumpy' SLSNe could belong to a different population. Weak correlations are observed between the peak luminosity and colour indices. No relationship is found between the UV peak magnitude and the decline rate, in contrast to what is typically found in the optical band. The correlations found here are promising, and give encouraging insights into the use of SLSNe as cosmological probes at high redshifts using standardizing relations in the UV. We also highlight the importance of early, and consistent, photometric data for constraining the light-curve properties.