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, $langle X_Rrangle$, mass, $langle X_Mrangle$, and density, $langle X_rhorangle$, caused by nearby objects. We find $langle X_Rrangle=1.009pm0.045$, 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 $langle X_Mrangle=1.031pm0.019$, which is larger than $langle X_Rrangle$ because of the strength of the effect of contaminating light on the radial velocity measurements of the host star. We find $langle X_rhorangle=0.995pm 0.046$: 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.
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