We used the optical and near-infrared imagers located on the Liverpool, the IAC80, and the William Herschel telescopes to monitor 18 M7-L9.5 dwarfs with the objective of measuring their rotation periods. We achieved accuracies typically in the range ±1.5-28 mmag by means of differential photometry, which allowed us to detect photometric variability at the 2σ level in the 50 per cent of the sample. We also detected periodic modulation with periods in the interval 1.5-4.4 h in 9 out of 18 dwarfs that we attribute to rotation. Our variability detections were combined with data from the literature; we found that 65 ± 18 per cent of M7-L3.5 dwarfs with v sin i ≥ 30 km s-1 exhibit photometric variability with typical amplitudes ≤20 mmag in the I band. For those targets and field ultracool dwarfs with measurements of v sin i and rotation period we derived the expected inclination angle of their rotation axis, and found that those with v sin i ≥ 30 km s-1 are more likely to have inclinations ≳40 deg. In addition, we used these rotation periods and others from the literature to study the likely relationship between rotation and linear polarization in dusty ultracool dwarfs. We found a correlation between short rotation periods and large values of linear polarization at optical and near-infrared wavelengths.