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The quasifree $$\overrightarrow{\gamma } d\rightarrow \pi ^0n(p)$$ photon beam asymmetry, $$\varSigma $$, has been measured at photon energies, $$E_\gamma $$, from 390 to 610 MeV, corresponding to center of mass energy from 1.271 to 1.424 GeV, for the first time. The data were collected in the A2 hall of the MAMI electron beam facility with the Crystal Ball and TAPS calorimeters covering pion center-of-mass angles from 49$$^\circ $$ to 148$$^\circ $$. In this kinematic region, polarization observables are sensitive to contributions from the $$\varDelta (1232)$$ and N(1440) resonances. The extracted values of $$\varSigma $$ have been compared to predictions based on partial-wave analyses (PWAs) of the existing pion photoproduction database. Our comparison includes the SAID, MAID and Bonn–Gatchina analyses; while a revised SAID fit, including the new $$\varSigma $$ measurements, has also been performed. In addition, isospin symmetry is examined as a way to predict $$\pi ^0n$$ photoproduction observables, based on fits to published data in the channels $$\pi ^0p$$, $$\pi ^+n$$ and $$\pi ^-p$$