Chief nurse Sherree Fagge urged people with less urgent or minor illnesses and injuries to consider alternatives to the emergency departments, such as the BrightonStation Health Centre.
The anniversary year was being launched on Saturday night at the museum, which occupies Victorian arches in Trafalgar Street, underneath Brighton railway station.
Both groups of protesters gathered at assigned locations outside Brighton railway station at about midday, marching along separate routes, guided by police to Victoria Gardens.