Jeremy Hunt has insisted Brexit negotiations have made "enormous progress", despite continued deadlock over plans for a customs backstop and growing Tory fury at Theresa May's plans.
The foreign secretary said it was a sign of success that most of a deal is now in place, despite there being only weeks left to reach an agreement on the backstop, which has been the sticking point in negotiations for months,
It comes as Tory MPs attacked Ms May's suggestion that the transition period could be extended, and EU leaders admitted they would have to help the prime minister force a deal through parliament.
Despite growing fears that Britain could crash out of the EU, Mr Hunt said the fact that the lack of agreement on the customs backstop was the "only really big outstanding issue" was a cause for celebration.
He told BBC Radio 4's Today programme: "I think it is important to say that, four weeks before the November deadline that's been talked about, this is actually the only really big outstanding issue, and so we have made enormous progress."
Mr Hunt said he was confident a deal will be agreed, pointing to comments by Angela Merkel, the German chancellor, that "where there's a will there's a way."
He said: "It would be entirely possible to agree a EU-wide solution to this issue, but not one that means indefinite membership of the customs union, if there was a willingness to do it.
"We will never agree to a solution that leads to the break-up of the United Kingdom. The EU know that extremely well and Theresa May has been very, very clear on that."
The EU is willing to accept a backstop that would see the entire UK retain, but also wants a fall-back option that would apply only to Northern Ireland. The UK government has ruled this out, leading to gridlock in talks.
Ms May this week suggested that extending the Brexit transition period could be an agreement on the backstop.
That triggered an angry backlash from Eurosceptic and pro-EU Tory MPs alike, with former Tory leader Iain Duncan Smith, a Brexiteer, claiming the government's strategy was "more like capitulation than negotiation".
Mr Hunt defended suggestions the period could be extended, saying: "There is a situation where you've negotiated a free trade agreement and it's going to take a few months more to implement - months not years - when it might be helpful to have the ability to extend the transition period."
His comments come amid reports the EU is are prepared to help Ms May get her Brexit plan through Parliament.
Jean-Claude Juncker, president of the European Commission, reportedly told EU leaders they would need to assist the prime minister with convincing MPs to support the deal she brings back from Brussels.
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