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."
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.
"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."
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.
