  We investigate the connection between galaxy--galaxy mergers and enhanced
black hole (BH) growth using the cosmological hydrodynamical EAGLE simulation.
We do this via three methods of analysis, investigating: the merger fraction of
AGN, the AGN fraction of merging systems and the AGN fraction of galaxies with
close companions. In each case, we find an increased abundance of AGN within
merging 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 subset
of the galaxy population. The greatest excess of AGN triggered via a merger are
found in lower mass ($M_* \sim 10^{10}$~\Msol) gas rich ($f_{\mathrm{gas}} >
0.2$) central galaxies with lower mass BHs ($M_{\mathrm{BH}} \sim
10^{7}$~\Msol) at lower redshifts ($z<1$). We find no enhancement of AGN
triggered via mergers in more massive galaxies ($M_* \gtrsim 10^{11}$~\Msol).
The enhancement of AGN is not uniform throughout the phases of a merger, and
instead peaks within the early \emph{remnants} of merging systems (typically
lagging $\approx 300$~Myr post-coalescence of the two galaxies at $z=0.5$). We
argue 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 BH
masses globally. Whilst at all redshifts the galaxies experiencing a merger
have 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 a
merger. We compute that on average no more than 15\% of a BHs final day mass
comes from the enhanced accretion rates triggered via a merger
