The beam attenuation by two-photon absorption in thin crystals and glass plates is utilized for directly measuring the intensity autocorrelation of UV femtosecond pulses without the need for an auxiliary pulse. We give a full description of the newly developed setup for operation from the blue down to the deep UV. The conditions that must be met to achieve reliable measurements are investigated. The choice of the two-photon absorbing material governs the attainable wavelength range, the material thickness determines the shortest pulse that can be reliably characterized, and high intensities influence the derived pulse duration due to saturation effects. The performance of the UV autocorrelator is demonstrated for pulses with durations below 20 fs, with energies of 3 nJ and with central wavelengths from the visible down to 195 nm. 2 Hz update rates are achieved at the 1 kHz repetition rate of the laser. The wavelength dependence of the two-photon absorption coefficient of BBO is determined by z-scan measurements and we find that it decreases much faster at longer wavelengths than is expected from the linear absorption spectrum.