  We used photometric data from the WASP (Wide-Angle Search for Planets) survey
to explore the possibility of detecting eclipses and transit signals of brown
dwarfs, gas giants and terrestrial companions in close orbit around white
dwarfs. We performed extensive Monte Carlo simulations and we found that for
Gaussian random noise WASP is sensitive to companions as small as the Moon
orbiting a $V\sim$12 white dwarf. For fainter stars WASP is sensitive to
increasingly larger bodies. Our sensitivity drops in the presence of co-variant
noise structure in the data, nevertheless Earth-size bodies remain readily
detectable in relatively low S/N data. We searched for eclipses and transit
signals in a sample of 194 white dwarfs in the WASP archive however, no
evidence for companions was found. We used our results to place tentative upper
limits to the frequency of such systems. While we can only place weak limits on
the likely frequency of Earth-sized or smaller companions; brown dwarfs and gas
giants (radius$\simeq$ R$_{jup}$) with periods $\leq$0.2 days must certainly be
rare ($<10\%$). More stringent constraints requires significantly larger white
dwarf samples, higher observing cadence and continuous coverage. The short
duration of eclipses and transits of white dwarfs compared to the cadence of
WASP observations appears to be one of the main factors limiting the detection
rate in a survey optimised for planetary transits of main sequence stars.
