The issue has become a political and sporting battleground, with the Scottish, Welsh and Irish football associations opposing a joint squad in case it affects the future of their independent national sides.
Sutcliffe told MPs he wanted a team which had the "widest representation" from the UK, but it could be that only the Football Association in England would allow its players to compete.
Prime Minister Gordon Brown has said he wants to see both male and female teams playing in the 2012 games.
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Mr Sutcliffe said football's international ruling body FIFA had given written assurances that a UK side in 2012 would not affect the national teams.
But he acknowledged "there has always been and will continue to be a threat to that individuality because of the way FIFA is evolving", irrespective of the 2012 issue.
Speaking in a debate at Parliament's Westminster Hall he said: "What a farce it would be to have those qualification games in Wales and Scotland without the possibility of British participation."
Asked if a purely English team would take the field if the associations in the other home nations boycotted the event, Mr Sutcliffe said: "That is correct and that is the sad fact of what is going to happen unless we can try and resolve this issue."
The debate was opened by the SNP's Pete Wishart (Perth and N Perthshire), who said participation in the "meaningless" Olympic soccer competition could jeopardise the future of the Scotland national side.
He said: "We should do absolutely nothing that would ever threaten our independent football status.
"We should never give a hint of a precedent that might be able to be used against us in the future, we should give no reason, no excuse to those who would question our independent footballing status, no succour to those who would seek to end the very generous arrangements we have in the UK."
Competing in the Olympics would risk that status for "a meaningless competition and I say it is not worthwhile".
He also claimed the Prime Minister had been leading calls for a joint team for political reasons, as part of his "Britishness agenda".
Labour's Albert Owen (Ynys Mon) accused the SNP and Plaid Cymru of pursuing a "narrow nationalist agenda" in opposing the joint team.
His fellow Labour backbencher Andrew Mackinlay (Thurrock) supported the objective of a joint team but said it was a matter for the football associations to decide and "the Government should back off".
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