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We investigate the connection between galaxy--galaxy mergers and enhancedblack hole (BH) growth using the cosmological hydrodynamical EAGLE simulation.We do this via three methods of analysis, investigating: the merger fraction ofAGN, the AGN fraction of merging systems and the AGN fraction of galaxies withclose companions. In each case, we find an increased abundance of AGN withinmerging systems relative to control samples of inactive or isolated galaxies(by up to a factor of $\approx 3$ depending on the analysis method used),confirming that mergers are enhancing BH accretion rates for at least a subsetof the galaxy population. The greatest excess of AGN triggered via a merger arefound in lower mass ($M_* \sim 10^{10}$~\Msol) gas rich ($f_{\mathrm{gas}} >0.2$) central galaxies with lower mass BHs ($M_{\mathrm{BH}} \sim10^{7}$~\Msol) at lower redshifts ($z<1$). We find no enhancement of AGNtriggered via mergers in more massive galaxies ($M_* \gtrsim 10^{11}$~\Msol).The enhancement of AGN is not uniform throughout the phases of a merger, andinstead peaks within the early \emph{remnants} of merging systems (typicallylagging $\approx 300$~Myr post-coalescence of the two galaxies at $z=0.5$). Weargue that neither major ($M_{\mathrm{*,1}} / M_{\mathrm{*,2}} \geq\frac{1}{4}$) nor minor mergers ($\frac{1}{10} < M_{\mathrm{*,1}} /M_{\mathrm{*,2}} < \frac{1}{4}$) are statistically relevant for enhancing BHmasses globally. Whilst at all redshifts the galaxies experiencing a mergerhave accretion rates that are on average 2--3 times that of isolated galaxies,the majority of mass that is accreted onto BHs occurs outside the periods of amerger. We compute that on average no more than 15\% of a BHs final day masscomes from the enhanced accretion rates triggered via a merger

Galaxy mergers in EAGLE do not induce a significant amount of black hole growth yet do increase the rate of luminous AGN