Mr Lidington, Prime Minister Theresa May’s de facto deputy, said that indifference in England was a threat to the Union.
Asked if the UK could survive as one country if it quit the EU without an agreement, the Cabinet Office Minister told BBC Radio 4’s World At One: “I think the UK would be under much greater strain in the event of a no deal.”
Mr Lidington, who backs Foreign Secretary Jeremy Hunt in the Tory leadership campaign, added: “The Union is under greater strain than I have ever seen in my lifetime.
“The threat to the Union, in my view, comes not just from Scottish nationalism, or pressure for Irish unification, it comes from indifference amongst English opinion to the value of the Union.
“I think there is a sense in which we take the Union for granted.
“And, sometimes I think there are too many people in England, including in my party, who assume that you can be dismissive of the contribution that Scotland or Northern Ireland makes.”
Mr Lidington’s remarks are likely to be seen by some at Westminster as a thinly veiled dig at Boris Johnson who has insisted the UK must quit the EU with or without a deal on October 31.
The comments came as Mrs May was using a speech in Scotland to say the next prime minister will make strengthening the Union their top priority.