A method for disinfecting a surface contaminated with microorganisms or suspected of being contaminated with microorganisms, the microorganism being one or more of Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa, and Enterococcus hirae, including the step of contacting the surface with a disinfecting composition including: 0.1-10 wt. % of one or more N-acylated amino acids or N-acylated peptides, or a salt thereof, less than 0.1 wt. % of hydrogen peroxide, 0.1-20 wt. % of one or more non-ethoxylated anionic surfactants, 0.05-5 wt. % of a carboxylic acid, wherein the disinfecting composition has a pH in the range of 1-4.5 wherein the composition includes less than 5 wt. % of ethoxylated anionic surfactant. The invention also pertains to a composition suitable for use in the method according to the invention. The method and composition provide excellent biocidal activity over a broad range of organisms using low concentrations of organic acids.