Ion bursts, accelerated by an ultrafast (40 fs) laser-assisted target normal sheath acceleration mechanism, can be adjusted so as to deliver a nearly pure proton beam. Such laser-driven proton bursts have predominantly a low transverse emittance and a broad kinetic spectrum suitable for continuous probing of the temporal evolution of spatially extended electric fields that arise after laser irradiation of thin foils. Fields with a strength of up to 10¹⁰ V/m were measured with a new streaklike proton deflectometry setup. The data show the temporal and spatial evolution of electric fields that are due to target charge-up and ion-front expansion following intense laser-target interaction at intensities of 10¹⁷-10¹⁸ W/cm². Measurement of the field evolution is important to gain further insight into lateral electron-transport processes and the influence of field dynamics on ion beam properties.