Using a picosecond image converter camera with a linear sweep (PS-1/S1 streak camera developed at GPI RAS, Moscow), we have measured temporal parameters of Vavilov – Cherenkov radiation pulses. The radiation was generated by relativistic electrons passing through a quartz cone mounted on the axis of a vacuum chamber of a linear accelerator, which is a part of the VEPP-5 injection complex at the Budker Institute of Nuclear Physics, Siberian Branch of the Russian Academy of Sciences (BINP SB RAS, Novosibirsk). The data obtained in these experiments provide an insight into the processes of formation of electron bunches and their ‘quality’ in a linear accelerator prior to injection of electrons into the accumulator-cooler. A conclusion is made regarding the advisability of streak camera application in tuning the linear accelerators for optimisation of electron bunch parameters.