This is the accepted version of the following article: Cuadra, J. and Meir, E. (2019), Non‐existence of Hopf orders for a twist of the alternating and symmetric groups. J. London Math. Soc., which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12203.