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.