Meanwhile, the Sunday Express says senior Government figures have warned that "Brexit is dead" - although Brexiteers have vowed to keep fighting until the United Kingdom leaves the EU.
Labour has called for a new permanent customs union with the EU - something the UK Prime Minister Theresa May has repeatedly ruled out.
Meanwhile, an analysis of various polls by the Sunday Telegraph showed that the Tories would lose almost 60 seats in a potential snap election that could come over May's failure to deliver on Brexit.
Members of a new political party founded by former UKIP leader Nigel Farage are gathering for their first rally on the south coast.
Labour would increase its number of MPs by 34, making them the largest party in the British parliament.
Britain was due to have left the EU earlier European elections in May.
Eurosceptic Iain Duncan Smith, a former Conservative Party leader, said May should be ready to quit in June.
David Lidington, who is leading the talks with Labour on subjects such as environmental standards, workers rights and the security relationship with the European Union, said the discussions were going to continue next week but that they wouldn't last months.
"I think what matters is that we have a cabinet that believes in Brexit, and we believe in Brexit, whichever way we voted in the referendum, because we're all democrats and we think that there are great opportunities for this country, whichever choice it makes", Hunt told BBC Radio 4's Today programme from Japan, where he met the Japanese prime minister, Shinzo Abe.
Despite the best efforts by Remainers to use European Parliament elections to their advantage, think tank Open Europe said last week that the polls are likely to result in a "protest" vote, where Britons will "send a message" to the establishment, punishing them for failing to deliver Brexit.
"If we're going to reach an agreement on this there's going to need to be movement from both sides", he said.
Last week, the European Union agreed a new Brexit deadline of 31 October.
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