We report a new method using high-stability, laser-driven supercontinuum generation in a liquid cell to calibrate the absolute photon response of fast optical streak cameras as a function of wavelength when operating at fastest sweep speeds. A stable, pulsed white light source based around the use of self-phase modulation in a salt solution was developed to provide the required brightness on picosecond time scales, enabling streak camera calibration in fully dynamic operation. The measured spectral brightness allowed for absolute photon response calibration over a broad spectral range (425-650 nm). Calibrations performed with two Axis Photonique streak cameras using the Photonis P820PSU streak tube demonstrated responses that qualitatively follow the photocathode response. Peak sensitivities were one photon/count above background. The absolute dynamic sensitivity is less than the static by up to an order of magnitude. We attribute this to the dynamic response of the phosphor being lower.