We exploit the phenomenon of resonant dispersive wave (RDW) emission in gas-filled hollow capillary fibres (HCFs) to realize time-resolved photoelectron imaging (TRPEI) measurements with an extremely short temporal resolution. By integrating the output end of an HCF directly into a vacuum chamber assembly we demonstrate two-colour deep ultraviolet (DUV)-infrared instrument response functions of just 10 and 11 fs at central pump wavelengths of 250 and 280 nm, respectively. This result represents an advance in the current state of the art for ultrafast photoelectron spectroscopy. We also present an initial TRPEI measurement investigating the excited-state photochemical dynamics operating in the N-methylpyrrolidine molecule. Given the substantial interest in generating extremely short and highly tuneable DUV pulses for many advanced spectroscopic applications, we anticipate our first demonstration will stimulate wider uptake of the novel RDW-based approach for studying ultrafast photochemistry – particularly given the relatively compact and straightforward nature of the HCF setup.