The 54,357 spectators gathered at Twickenham, a record for the series' 12-year history, had little to celebrate as the hosts managed only one win from three games in Group B.
England survived a scare to beat the United States in their opener. Ben Gollings was generously awarded an early try after he appeared to drop the ball forward over the line and Tom Powell went in for a second score with Gollings landing both conversions, the second a superb effort from the left touchline.
Matt Hawkins and Paul Emerick levelled the scores by half-time and Shalom Suniula burst clear to score under the posts and converted to give the USA a shock 21-14 lead, but Dan Norton hit back with a quickfire hat-trick to seal a 31-21 win.
A late try from France's Mathieu Acebes condemned England to a 21-14 defeat second time out. Gollings had scored two tries and two conversions, sandwiching scores from France's Jean Baptiste Gobelet and Paul Albaladejo, but Acebes struck after a length-of-the-field break.
That meant only a win over Argentina would secure a quarter-final spot in the main cup competition, and a 12-12 draw left Ben Ryan's side facing a bowl clash with Kenya as Argentina instead prepare to face New Zealand.
Reigning Rugby World Cup Sevens champions Wales qualified as Group A runners-up, hammering Spain 33-10 in their opening game and adding a second comfortable win, 29-12 over Kenya, to set up a shoot-out for top spot with New Zealand.
They could not live with the Kiwis though, a 31-12 defeat leaving them second and facing France in the next round. New Zealand had beaten Kenya 28-12 and Spain 40-7 to top the group, and England's failings sealed their series triumph.
Scotland finished rock bottom of Group C, acquitting themselves well in narrow defeats to Samoa (19-15) and group winners Australia (24-21) but finishing with a dismal 25-12 defeat to minnows Canada. They will face Portugal in the bowl quarter-final.
Fiji edged out South Africa 12-7 to claim top spot in Group D and will face Samoa in Sunday's quarter-finals, with the Vipers awaiting Australia in the marquee last-eight clash.
The crowd figure represented the one positive for England and Rugby Football Union business operations director Paul Vaughan said: "The first-day record is a testimony to the booming global popularity of sevens.
"We hope a good second day will take a sevens weekend past the 100,000 mark for the first time, which would be a magnificent achievement."
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