Context : Gravitational wave ( GW ) astronomy has rapidly reached maturity becoming a fundamental observing window for modern astrophysics . The coalescences of a few tens of black hole ( BH ) binaries have been detected , while the number of events possibly including a neutron star ( NS ) is still limited to a few . On 2019 August 14 , the LIGO and Virgo interferometers detected a high-significance event labelled S190814bv . Preliminary analysis of the GW data suggests that the event was likely due to the merger of a compact binary system formed by a BH and a NS , although the lighter object could still be consistent with being a low-mass BH . Aims : In this paper , we present our extensive search campaign aimed at uncovering the potential optical/near infrared electromagnetic counterpart of S190814bv . We found no convincing electromagnetic counterpart in our data . We therefore use our non-detection to place limits on the properties of the putative outflows that could have been produced by the binary during and after the merger . Methods : Thanks to the three-detector observation of S190814bv , and given the characteristics of the signal , the LIGO and Virgo Collaborations delivered a relatively narrow localisation in low latency – a 50 % ( 90 % ) credible area of 5 \mathrm { deg } ^ { 2 } ( 23 \mathrm { deg } ^ { 2 } ) – despite the relatively large distance of 267 \pm 52 Mpc . ElectromagNetic counterparts of GRAvitational wave sources at the VEry Large Telescope ( ENGRAVE ) collaboration members carried out an intensive multi-epoch , multi-instrument observational campaign to identify the possible optical/near infrared counterpart of the event . In addition , the ATLAS , GOTO , GRAWITA-VST , Pan-STARRS and VINROUGE projects also carried out a search on this event . In this paper , we describe the combined observational campaign of these groups . Results : Our observations allow us to place limits on the presence of any counterpart and discuss the implications for the kilonova ( KN ) possibly generated by this NS-BH merger , and for the strategy of future searches . The typical depth of our wide-field observations , which cover most of the projected sky localisation probability ( from 33 % to 99.8 % , depending on the night and filter considered ) , is r \sim 22 ( resp . K \sim 21 ) in the optical ( resp . near infrared ) . We reach deeper limits in a subset of our galaxy-targeted observations , which cover a total \sim 50 \% of the galaxy-mass-weighted localisation probability . Altogether , our observations allow us to exclude a KN with large ejecta mass M \gtrsim 0.1 \mathrm { M _ { \odot } } to a high ( > 90 \% ) confidence , and we place meaningful limits on a larger portion of the ejecta mass parameter space . This disfavours the tidal disruption of the neutron star during the merger . Conclusions : Despite the sensitive instruments involved in the campaign , given the distance of S190814bv we could not reach sufficiently deep limits to constrain a KN comparable in luminosity to AT 2017gfo on a large fraction of the localisation probability . This suggests that future ( likely common ) events at a few hundreds Mpc will be detected only by large facilities with both high sensitivity and large field of view . Galaxy-targeted observations can reach the needed depth over a relevant portion of the localisation probability with a smaller investment of resources , but the number of galaxies to be targeted in order to get a fairly complete coverage is large , even in the case of a localisation as good as that of this event .