We analyse the evolution of environmental quenching efficiency, the fraction of quenched cluster galaxies which would be star forming if they were in the field, as a function of redshift in 14 spectroscopically confirmed galaxy clusters with 0.87 < z < 1.63 from the Spitzer Adaptation of the Red-Sequence Cluster Survey. The clusters are the richest in the survey at each redshift. Passive fractions rise from 42+10−13 per cent at z ∼ 1.6 to 80+12−9 per cent at z ∼ 1.3 and 88+4−3 per cent at z < 1.1, outpacing the change in passive fraction in the field. Environmental quenching efficiency rises dramatically from 16+15−19 per cent at z ∼ 1.6 to 62+21−15 per cent at z ∼ 1.3 and 73+8−7 per cent at z ≲ 1.1. This work is the first to show direct observational evidence for a rapid increase in the strength of environmental quenching in galaxy clusters at z ∼ 1.5, where simulations show cluster-mass haloes undergo non-linear collapse and virialization. [ABSTRACT FROM AUTHOR]