This Letter presents direct searches for lepton flavour violation in Higgs boson decays, $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, performed with the ATLAS detector at the LHC. The searches are based on a data sample of proton-proton collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 36.1 fb$^{-1}$. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95% confidence-level upper limits are 0.47% (0.34$^{+0.13}_{-0.10}$%) and 0.28% (0.37$^{+0.14}_{-0.10}$%) for $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, respectively.

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