England went to the tournament in South Africa with high hopes but went out in the second round on Sunday when Germany trounced them 4-1 in Bloemfontein, their worst World Cup finals defeat.
Conservative lawmaker David Amess said on his website that he was so appalled by England's performance that he filed a parliamentary motion demanding action.
The motion urges parliament to voice "its great disappointment at England's pathetic exit from the World Cup finals" and says the team "let this country and their supporters down."
It calls for an urgent inquiry into the state of the national game and says many players in England's highly-rated Premier League are "grossly overpaid and under-perform."
Football's governing body FIFA jealously guards the game from political interference.
FIFA President Sepp Blatter threatened on Tuesday to ban France's national and club teams from international competition if French politicians did not stop meddling in football affairs.
Amess's "early day motion" is one of hundreds filed by members of parliament (MPs) on a wide range of subjects. They are a kind of petition which other MPs can sign up to but they are not binding and often do not lead to any action.
So far, just one other MP, Liberal Democrat Mike Hancock, has backed Amess's motion.
The British media have savaged the England team for their lacklustre showing, criticised the sub-par performance of many of its stars, and called into question the future of the team's Italian coach Fabio Capello.
Many commentators say the Premier League takes precedence in England at the expense of the national team.
Britain is not the only country where poor results in South Africa have led to political repercussions.
A senior adviser to Nigerian President Goodluck Jonathan said on Wednesday he had suspended the side from international competition for two years following their poor performance in South Africa, where they went out in the first round.
France was consumed by a political inquest after the team finished bottom of its group.
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