Theresa May's de facto deputy said talks were at a "fork in the road" and that the only alternative to Britain crashing out of the bloc without an agreement was Brussels accepting the UK's proposals.
The Cabinet Office minister was speaking at a business conference in France, where he promised the UK would remain a "proud European nation" despite leaving the EU.
His speech marked part of a concerted effort by the UK government to persuade EU member states to back the Chequers plan despite opposition from officials in Brussels.
Speaking to the Mouvement des Entreprises de France (MEDEF) conference, Mr Lidington said: "With exactly seven months until the end of Article 50 process and less than two months ahead of the October European Council, we face the choice between the pragmatic proposals we are discussing now with the European Commission, or no deal.
"The alternative models do not meet the level of ambition or the outcome we all want to see delivered.
"So, we need the EU to engage with us on our positive vision of the future relationship."
He added: “I truly feel that we are at a fork in the road. There are trends on both sides of the Channel, both sides of the North Sea, and both sides of the Atlantic that could see us drift apart.”
UK ministers have made several attempts to convince France to back the Chequers plan, including Ms May flying to French president Emmanuel Macron's holiday home earlier this month in a bid to win him round.
Mr Lidington told French business leaders that European countries must work together to overcome "dark political forces" that have re-emerged on the continent.
He said: "I believe that this is a time when Europe, Europe inside the EU and Europe outside the EU, needs to pull together to embrace the spirit of unity and co-operation that has been the cause of our success for more than half a century.
"Even in Europe, dark political forces, long banished to the very fringes of society and the ashes of history, are re-emerging - feeding on resentment over inequality, stalling standards of living and rapid social change."
He added: "My government has been clear throughout our discussions with our European partners on our future relationship: we want a deep and special partnership with the EU, we remain a proud European nation committed to European values, European security and European trade.
"We are indispensable partners in an unpredictable world. Now is the opportunity to cement that partnership and face the future together."
It came as Mr Lidington's cabinet colleague, Dominic Raab, insisted he remained confident of reaching a deal.
Appearing in front of the House of Lords EU committee, the Brexit Secretary said: "I'm confident that a deal is within our sights. We're bringing ambition, pragmatism, energy and if, and I expect it will be, and if it is matched, we get a deal."
However, he admitted that the October deadline for an agreement could slip, with reports suggesting both the UK and the EU see November as a more realistic timeframe.
He said: "I think it is important as we enter the final phase of the negotiations in the lead up to the October council and the possibility that it may creep beyond that, we want to see some renewed energy.
"We're bringing the ambition and the substance of our white paper on the future relationship and also I think some pragmatism to try and go the extra mile to get the deal that I think is in both sides interests. We need that to be matched obviously, it's a negotiation."
Mr Raab will travel to Brussels later this week to resume talks with his EU counterpart, Michel Barnier.
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