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