Dan Norton's tries in the victories over France (28-0) and the USA (15-5) took him to 37 for the season, more than any Englishman has ever scored in a single Sevens World Series season.
The crowd of 60,050 was a sevens world record for a single day - beating last year's 54,357 Saturday attendance.
But the day ended on a flat note for England as they went down 14-7 against Samoa in their final Pool B match.
Wales failed to reach the last eight after a shock 22-7 defeat against Spain, who now take on Samoa.
New Zealand face South Africa and Australia tackle Argentina in the other quarter-finals.
A quarter-final win for New Zealand would clinch their 10th series title in 13 years while England can make sure of third place in the table if they can repeat their victory over Fiji at last weekend's Glasgow Sevens.
England head coach Ben Ryan said: "We did okay in our first two games but the last one was one of the ugliest I've been involved in. We probably played into their hands a bit.
"We'll go away and press the reset button. We've got a 4-1 winning record against Fiji this season and we're playing them in London with a home crowd behind us. We'll give it a really good crack."
Norton overhauled Rob Thirlby's 2003-04 record against France with Sam Edgerley (2) and Tom Mitchell adding further tries with Mitchell converting all four. Edgerley and Mitchell were also on target against the USA.
Against Samoa, England conceded first half tries to Taulagi Afamasaga and Tom Iosefo with Mat Turner scoring their consolation effort.
Wales had opened their account with a 19-12 win over Zimbabwe but were tripped up 22-7 by Spain - recognised as an emerging force in the sevens game - and were then thrashed 43-7 by Fiji.
Dan Fish got Wales' consolation try against Spain, having scored the clincher against Zimbabwe when Richard Smith and Rhys Jones also touched down. Smith also scored against the Fijians, who ran in seven scintillating tries.
Scotland had been pitched into a tough Pool D, going down 27-12 to Australia and 20-5 to South Africa.
Michael Fedo and Sean Kennedy scored tries in the first game, John Houston in the second.
They rallied from 12-0 down to beat Portugal 26-12 on their final outing with Fedo, Colin Gregor, James Fleming and Byron McGuigan scoring.
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