The Blitzboks could feel the effects of the truncated Hamilton leg of the World Sevens Series and miss out on the semi-finals even if they beat Kenya on Sunday morning.
Winning every single match at FMG Stadium Waikato is crucial as the quart-final stage of the tournament has been scrapped - meaning that only the top pool in each team will progress to the semis - but a 21-19 loss to England very well may have cost the South Africans that chance.
The Blitzboks showed great form early on in their second match after beating Japan, scoring two quick tries by captain Stedman Gans and JC Pretorius to go 14-0 up.
England responded with two tries of their own to level the scores, before Phil Burgess added a third to grab the lead for the first time in the match.
The Blitzboks visited England's in-goal again when Justin Geduld found a gap, but he missed the crucial conversion, taking to score to 19-21.
Earlier in the day, the Blitzboks secured an easy 35-5 win over Japan, with Angelo Davids getting a brace, while Muller du Plessis, Cecil Afrika and Pretorius all added five-pointers of their own.
The Blitzboks will face Kenya in their last pool game at 1.13 AM on Sunday.