Sutcliffe told a parliamentary debate that although he was hopeful of having the "widest representation" from Britain in the team it was now likely that only the English FA would allow its players to compete.
"What a farce it would be to have those qualification games in Wales and Scotland without the possibility of British participation," he said.
Asked if a purely English team would comprise the team if the other home nations refused to take part, he replied: " "That is correct and that is the sad fact of what is going to happen unless we can try and resolve this issue."
FIFA president Sepp Blatter has said a British team should only comprise English players to avoid jeopardizing the status of Northern Ireland, Wales and Scotland.
However, he has also pointed out that the independent status of the four countries is enshrined in FIFA's statutes and will never be changed.
Although the four British associations are recognized as separate entities by FIFA, the International Olympic Committee recognises Britain only as an entity to compete in the Olympics.
NO THREATS
Pete Wishart of the Scottish National Party said the Olympic soccer tournament was a meaningless competition but one that could jeopardise the future of the Scotland national side.
"I can stand here today and try and defend our national football team. If we took a decision that threatened that team, even if it was a one in a 100 chance, or one in a 1,000 chance it should be dismissed out of hand.
"We should do absolutely nothing that would ever threaten our independent football status."
The English FA committed itself to entering a team in the Olympics last August with both its chairman David Triesman and its then chief executive Brian Barwick backing the plan.
Britain, Olympic champions in 1908 and 1912, have not played in the men's Olympic soccer finals since 1960 and have never entered a women's team because of concerns from the other home nations regarding their status.
The Olympic football tournament mainly comprises players aged Under-23 although up to three over-aged players are allowed to take part.
