  We perform a detailed study of six transiting planetary systems with
relatively bright stars close enough to affect observations of these systems.
Light curves are analysed taking into account the contaminating light and its
uncertainty. We present and apply a method to correct the velocity amplitudes
of the host stars for the presence of contaminating light. We determine the
physical properties of six systems (WASP-20, WASP-70, WASP-8, WASP-76, WASP-2
and WASP-131) accounting for contaminating light. In the case of WASP-20 the
measured physical properties are very different for the three scenarios
considered (ignoring binarity, planet transits brighter star, and planet
transits fainter star). In the other five cases our results are very similar to
those obtained neglecting contaminating light. We use our results to determine
the mean correction factors to planet radius, $\langle X_R\rangle$, mass,
$\langle X_M\rangle$, and density, $\langle X_\rho\rangle$, caused by nearby
objects. We find $\langle X_R\rangle=1.009\pm0.045$, which is smaller than
literature values because we were able to reject the possibility that the
planet orbits the fainter star in all but one case. We find $\langle
X_M\rangle=1.031\pm0.019$, which is larger than $\langle X_R\rangle$ because of
the strength of the effect of contaminating light on the radial velocity
measurements of the host star. We find $\langle X_\rho\rangle=0.995\pm 0.046$:
the small size of this correction is due to two effects: the corrections on
planet radius and mass partially cancel; and some nearby stars are close enough
to contaminate the light curves of the system but not radial velocities of the
host star. We conclude that binarity of planet host stars is important for the
small number of transiting hot Jupiters with a very bright and close nearby
star, but it has only a small effect on population-level studies of these
objects.
