Lichfield and Burntwood’s MP has vowed to fight for a third referendum if a second Brexit vote takes place.
Campaigners have called for a People’s Vote to give people a fresh chance to have their say on leaving the European Union.
Labour has also said it would support a second referendum, adding weight to the calls for another poll.
But Conservative MP Michael Fabricant said the result would leave the country no closer to a definitive decision.
In a column for The Sun, Mr Fabricant said: “If the result of the first referendum can be overturned, is it not right that the electorate then have the chance to overrule the second as well?
“After all, one of the main arguments by proponents of a People’s Vote is that ‘facts change’. Which is true. But then, it follows that the facts will inevitably change again in a few years’ time.
“If this second referendum were to take place, what would happen if Remain wins a narrow victory – and it is unlikely it would be anything more than narrow?
“We would then be left with a difficult situation: two votes, two different results, yet with one result being carried through and the other ignored.”