England scored an ignominious double on Monday, becoming the first country to be dumped out of Europe twice in a week and in the process losing both its prime minister and national soccer team manager.

Just days after English voters steered the United Kingdom towards a "Brexit" from the European Union, England provided another shock, crashing out of the Euro 2016 soccer competition to Iceland - the smallest country ever to appear in a major tournament.

"We embarrassed ourselves three of four days ago in the referendum, we've embarrassed ourselves now. It's a really, really sad time to be English," lamented English soccer fan Alex in the French city of Nice.

"Brexit2" quickly became a top trending topic on Twitter after Iceland, with its population of just 332,000 people, beat England's bevy of highly paid players 2-1.

"The beautiful Irony. #England knocked out of #Euro2016 by country not even in the EU! Maybe that's why they pressed the #Brexit button," joked one Twitter user.

Manager Roy Hodgson resigned within minutes, following hot on the heels of Prime Minister David Cameron who quit on Friday after the vote to leave the EU.

The referendum result stunned European leaders, sent the British pound to multi-decade lows, and cost Britain its AAA credit rating. Experts called it the biggest blow to the EU project since its inception after World War Two.

The response to the soccer shock was dramatic too as fans contemplated the 50th anniversary of England's 1966 World Cup win in about one month's time.

Pundits ranked the defeat for a country that claims to have invented the game and is ranked 11th in the world among the worst since it lost to the amateurs of the United States in the 1950 World Cup.

"Mon dieu! Brexit X2 in a week from hell. Exit Europe, lose AAA rating, lose to Iceland in #Euro2016 utter nightmare! #Brexit2," mocked one French Twitter user.

Jokes also proliferated online about petitions being set up to get the match replayed - a mirror of the online campaign to get the referendum vote overturned by Parliament.

One suggested Hodgson should take over from Cameron because he would be the perfect man to lead the country out of Europe.

Another suggested the cost of the England squad should be spent on Britain's NHS public health service, a reference to the campaign promise by the "Brexit" camp that cash sent by London to Brussels each week would now be directed to the NHS instead. The Brexit team has rowed back on that pledge since winning.

"The England squad costs £175m. Let's spend it on the NHS," said Twitter user @AndrewBloch.

Fans of Britain's European neighbours were quick to see the link.

"Both are embarrassing. Iceland really deserved the win. They played amazing football and England were completely overwhelmed for all their arrogance with their fans everywhere," said Benjamin Rimaud, 22, an Irishman from Dublin whose father is French, and who watched the game in a Paris bar.

"As far as the referendum is concerned it's embarrassing too. I don't think they realised what they were letting themselves in for."