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This paper presents combined ${\it Spitzer}$ IRAC and ${\it Hubble}$ COSresults for a double-blind survey of 195 single and 22 wide binary white dwarfsfor infrared excesses and atmospheric metals. The selection criteria includecooling ages in the range 9 to 300 Myr, and hydrogen-rich atmospheres so thatthe presence of atmospheric metals can be confidently linked to ongoingaccretion from a circumstellar disc. The entire sample has infrared photometry,whereas 168 targets have corresponding ultraviolet spectra. Three stars withinfrared excesses due to debris discs are recovered, yielding a nominalfrequency of $1.5_{-0.5}^{+1.5}$ per cent, while in stark contrast, thefraction of stars with atmospheric metals is $45\pm4$ per cent. Thus, only oneout of 30 polluted white dwarfs exhibits an infrared excess at 3-4 $\mu$m inIRAC photometry, which reinforces the fact that atmospheric metal pollution isthe most sensitive tracer of white dwarf planetary systems. The correspondingfraction of infrared excesses around white dwarfs with wide binary companionsis consistent with zero, using both the infrared survey data and an independentassessment of potential binarity for well-established dusty and polluted stars.In contrast, the frequency of atmospheric pollution among the targets in widebinaries is indistinct from apparently single stars, and moreover themultiplicity of polluted white dwarfs in a complete and volume-limited sampleis the same as for field stars. Therefore, it appears that the delivery ofplanetesimal material onto white dwarfs is ultimately not driven by stellarcompanions, but by the dynamics of planetary bodies.

The unbiased frequency of planetary signatures around single and binary white dwarfs using ${\it Spitzer}$ and ${\it Hubble}$