Abstract This paper presents a study of $$Z \rightarrow ll\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>→</mml:mo> <mml:mi>l</mml:mi> <mml:mi>l</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> decays with the ATLAS detector at the Large Hadron Collider. The analysis uses a proton–proton data sample corresponding to an integrated luminosity of 20.2 fb $$^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow /> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> collected at a centre-of-mass energy $$\sqrt{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 8 TeV. Integrated fiducial cross-sections together with normalised differential fiducial cross-sections, sensitive to the kinematics of final-state QED radiation, are obtained. The results are found to be in agreement with state-of-the-art predictions for final-state QED radiation. First measurements of $$Z \rightarrow ll\gamma \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>→</mml:mo> <mml:mi>l</mml:mi> <mml:mi>l</mml:mi> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> decays are also reported.