Daniel Sturridge was the only Reds player to make the starting line-up and it was his early through-ball that set Raheem Sterling on his way to win the penalty that Wayne Rooney dispatched to give the Three Lions a third-minute lead.
But that advantage lasted just two minutes as Ragnar Sigurdsson levelled with a header before Kolbeinn Sigthorsson's shot on 18 minutes squirmed through the arms of Joe Hart to put Iceland 2-1 ahead.
From there, former Reds boss Roy Hodgson - who resigned from his post as England boss shortly after full-time - could not engineer a comeback as they crashed out in a result labelled by some as the country's worst ever on a major tournament stage.
Adam Lallana, who had been pictured with his ankle wrapped in ice earlier in the week, was an unused substitute, as were club teammates Nathaniel Clyne, James Milner and Jordan Henderson as England suffered total humiliation at the hands of an excellently-organised Iceland team.
That means the quintet will return to Merseyside earlier than first thought, with pre-season training set to begin on July 2 ahead of a first friendly just six days later. They will return to the camp a little later, after a few weeks off, but will have a decent pre-season as Jürgen Klopp looks to bring his side up to scratch.
Allen helps Wales through to set up Belgium clash
Otherwise, Belgian trio Divock Origi, Christian Benteke and Simon Mignolet were all unused substitutes as Belgium put four goals past Group F winners Hungary in a ruthless romp in Toulouse on Sunday.
Chelsea's Eden Hazard starred as goals from Toby Alderweireld, Michy Batshuayi, Hazard himself and Yannick Ferreira Carrasco saw Marc Wilmots' men into the next round.
Joe Allen helped Wales to the quarter-finals of the European Championsips at their first ever tournament as they overcame Northern Ireland in a game dubbed 'the Battle of Britain.'
Gareth McAuley turned Gareth Bale's cross into his own goal with 15 minutes remaining for the game's only goal, setting Wales up with a huge last eight clash against Mignolet, Origi and Benteke's Belgium. Danny Ward was once again an unused substitute.
Elsewhere, Emre Can has still yet to make an appearance for Germany at the tournament, though he will have been delighted with his international teammates' performances as they swept Martin Skrtel's Slovakia comfortably aside in a 3-0 win.
Skrtel was actually guilty of manhandling Mario Gomez to concede a penalty after 13 minutes, although he was fortunate to see Matus Kozacik save Mesut Ozil's spot-kick. But the Slovakians could not bounce back as Gomez and Julian Draxler heaped further misery on them after Jerome Boateng had opened the scoring.
Reds' Euros contingent cut by half after Round of 16
That means of the previous 12 Liverpool representatives at Euro 2016, only six remain in the quarter-finals - five of which meet as Belgium take on Wales in the last eight.
Emre Can's Germany look increasingly likely of reaching the latter stages - although they face a strong Italy team next time out, with Antonio Conte's side having thwarted Belgium in the group stages before dumping out holders Spain in the last round.
The elimination of Skrtel's Slovakia means he is now free to tie up his future, having said he would decide on his next destination after the end their campaign. He has been heavily linked with a move to Turkey having been told by Klopp that his Liverpool career is over.