In spite of its importance for the study of star formation at all mass domains, the nearby young sigma Orionis cluster still lacks a comprehensive survey for multiplicity. We try to fill that observational gap by looking for wide resolved binaries with angular separations between 0.4 and 4.0 arcsec. We search for companions to 331 catalogued cluster stellar members and candidates in public K-band UKIDSS images outside the innermost 1 arcmin, which is affected by the glare of the bright, eponymous sigma Ori multiple system, and investigate their cluster membership with colour-magnitude diagrams and previous knowledge of youth features. Of the 18 identified pairs, ten have very low individual probabilities of chance alignment (< 1 %) and are considered here as physical pairs. Four of them are new, while the other six had been discovered previously, but never investigated homogeneously and in detail. Projected physical separations and magnitude differences of the ten probably bound pairs range from 180 to 1220 au, and from 0.0 to 3.4 mag in K, respectively. Besides, we identify two cluster stars with elongated point spread functions. We determine the minimum frequency of wide multiplicity in the interval of projected physical separations s = 160-1600 au in sigma Orionis at 3.0^{+1.2}_{-1.1} %. We discover a new Lindroos system, find that massive and X-ray stars tend to be in pairs or trios, conclude that multiplicity truncates circumstellar discs and enhances X-ray emission, and ascribe a reported lithium depletion in a young star to unresolved binarity in spectra of moderate resolution. When accounting for all know multiples, including spectroscopic binaries, the minimum frequency of multiplicity increases to about 10 %, which implies that of the order of 80-100 unknown multiple systems still await discovery in sigma Orionis.
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