Context: Ultra-cool dwarfs of the L spectral type (T_eff = 1400-2200 K) are known to have dusty atmospheres. Asymmetries of the dwarf surface may arise from rotationally-induced flattening and dust-cloud coverage, and may result in non-zero linear polarisation through dust scattering. Aims: We aim to study the heterogeneity of ultra-cool dwarfs' atmospheres and the grain-size effects on the polarisation degree in a sample of nine late M, L and early T dwarfs. Methods: We obtain linear polarimetric imaging measurements using FORS1 at the Very Large Telescope, in the Bessel I filter, and for a subset in the Bessel R and the Gunn z filters. Results: We measure a polarisation degree of (0.31±0.06)% for LHS102BC. We fail to detect linear polarisation in the rest of our sample, with upper-limits on the polarisation degree of each object of 0.09% to 0.76% (95% of confidence level), depending on the targets and the bands. For those targets we do not find evidence of large-scale cloud horizontal structure in our data. Together with previous surveys, our results set the fraction of ultra-cool dwarfs with detected linear polarisation to 30+10_-6% (1-σ errors). From the whole sample of well-measured objects with errors smaller than 0.1%, the fraction of ultra-cool dwarfs with polarisation degree larger than 0.3% is smaller than 16% (95% confidence level). Conclusions: For three brown dwarfs, our observations indicate polarisation degrees different (at the 3-σ level) than previously reported, giving hints of possible variations. Our results fail to correlate with the current model predictions for ultra-cool dwarf polarisation for a flattening-induced polarisation, or with the variability studies for a polarisation induced by an heterogeneous cloud cover. This stresses the intricacy of each of those tasks, but may arise as well from complex and dynamic atmospheric processes. Based on observations collected at the European Observatory, Paranal, Chile, under programmes 075.C-0653(A) and 077.C-0819(A).