We present accurate ab initio non-perturbative calculations of the Breit correction to the parity non-conserving (PNC) amplitudes of the 6s−7s and 6s−5d 3/2 transitions in Cs, 7s−8s and 7s−6d 3/2 transitions in Fr, 6s − 5d 3/2 transition in Ba + , 7s − 6d 3/2 transition in Ra + , and 6p 1/2 − 6p 3/2 transition in Tl. The results for the 6s − 7s transition in Cs and 7s − 8s transition in Fr are in good agreement with other calculations while calculations for other atoms/transitions are presented for the first time. We demonstrate that higher-orders many-body corrections to the Breit interaction are especially important for the s − d PNC amplitudes. We confirm good agreement of the PNC measurements for cesium and thallium with the standard model .