England slipped into the bowl competition at the Tokyo Sevens after winning only one of their three Pool D matches.
A closing 31-7 win over Argentina was not enough to secure a quarter-final place after they squandered leads to lose 26-19 to Australia and 31-21 to Samoa.
Tries from Tom Powell, Christian Lewis-Pratt and Mathew Turner were in vain as Tom Cusack, Lewis Holland and Cameron Clark earned victory for Australia.
The pattern was repeated against Samoa as Lewis-Pratt, Dan Norton and John Brake gave England a 21-14 lead only for second-half tries from Lolo Lui, Tulolo Tulolo and Levi Asifamatala to turn the game around.
Norton, Sam Edgerley, Lewis-Pratt, Turner and Marcus Watson all crossed in a rout against Argentina but England face a bowl quarter-final against Portugal, bottom of Pool A.
Scotland will be Britain's sole representatives in the quarter-finals of the main competition after topping Pool B, winning 12-0 against Kenya and 12-10 against Wales before a closing 12-12 draw with the United States. Wales finished bottom of the group.