England started off well, beating Zimbabwe 24-7 with Wesley Mbanja's side offering little resistance but then quickly lost the plot against Kenya, losing 17-7.
They proceeded to put up a game fight against the reigning world sevens champions New Zealand, narrowly losing 26-24.
Paul Treu's quest to become the first South African coach in eight years to win the tournament was given a boost with a clinical showing, running Argentina ragged 24-7 in before sweeping aside Uganda 41-0.
They finished the night with a 31-0 demolition of Wales - who had earlier also lost to Argentina - to give themselves a good chance of winning the tournament.
Fiji were exceptional, conceding only 19 points in their three wins, and scoring 110 points on their way to the quarter-final stage.
Scotland had a well-earned 21-10 win over Australia but failed to find the same sort of form against Samoa before booking their place after a narrow win over Tunisia.
The Scots play South Africa in their quarter-final, while New Zealand face the USA and Argentina take on Samoa. The last quarter-final is between Fiji and Kenya.
England will face Canada in the Bowl quarter-final.