Context: Current atmospheric models cannot reproduce some of the characteristics of the transition between the L dwarfs with cloudy atmospheres and the T dwarfs with dust-depleted photospheres. It has been proposed that a majority of the L/T transition brown dwarfs could actually be a combinaison of a cloudy L dwarf and a clear T dwarf. Indeed binarity seems to occur more frequently among L/T transition brown dwarfs. Aims: We aim to refine the statistical significance of the seemingly higher frequency of binaries. Co-eval binaries would also be interesting test-beds for evolutionary models. Methods: We obtained high-resolution imaging for six mid-L to late-T dwarfs, with photometric distances between 8 and 33 pc, using the adaptive optics systems NACO at the VLT, and the Lick system, both with the Laser Guide Star. Results: We resolve none of our targets. Combining our data with published results, we obtain a frequency of resolved L/T transition brown dwarfs of 31^+21-15%, compared to 21^+10-7% and 14^+14-7% for mid-L and T dwarfs (90% of confidence level). These fractions do not significantly support, nor contradict, the hypothesis of a larger binary fraction in the L/T transition. None of our targets has companions with effective temperatures as low as 360-1000 K at separations larger than 0farcs5. Based on observations collected at the European Observatory, Paranal, Chile, under programmes 78.C-0754 and 79.C-0635.