While "Brexiteers" have strongly backed Mrs May's proposed clean break with the single market and customs union, finance minister Philip Hammond and others have this month echoed calls by businesses for less of a "hard Brexit" and retaining closer customs ties.
No deal would be "very, very bad" for Britain, Hammond said, but worse would be a deal "deliberately structured to punish us, to suck the lifeblood out of our economy".
Appearing on same program, Labour's Brexit spokesman Sir Keir Starmer said Britain woulc definitely leave the European Union, and that doind so would prevent it continuing as a full member of the single market.
With the Government having said it intends to withdraw from the European customs union, it is acknowledged "flexible and imaginative solutions" will be required to avoid a return to the "hard border" of the past, potentially undermining the Good Friday Agreement and the peace process.
"We will leave the customs union when we leave the European Union".
Jean-Claude Juncker: The European Commission president will not be directly involved in talks and his spokesman has said he is unlikely to spend more than half an hour a week on Brexit.
"If we're going to radically change the way we work together, we need to get there via a slope, not via a cliff edge", he said.
He added: "I don't care how we get it in terms of the structure as long as we get access to the single market tariff free and that means also we are not constrained by the existing rules of the single market and that's obviously freedom of movement".
Foreign Secretary Boris Johnson said Sunday if the negotiations are done right, it could present huge opportunities for Britain.
Labour's shadow Brexit secretary Sir Keir Starmer said the party would "leave options on the table" if it formed a government and took over negotiations in Brussels.
The government's plan for the next Parliament will be outlined in the Queen's speech on Wednesday, and will include laws needed to deliver Brexit and new immigration legislation.
"We are not turning our backs on Europe".
"If we had a strong signal that she were backsliding I think she would be in major difficulty", the newspaper quoted one unidentified former minister as saying. She's got no mandate here and she's got no authority overseas and the negotiation starts tomorrow.
The election debacle has left her weakened and fuelled speculation over her position.
Mr Davis said he would hammer out a "bold and ambitious deal" for the UK. That would mean future changes in laws affecting British citizens, including in relation to the ability of a spouse from overseas to join them in the United Kingdom, would affect European Union citizens as well, leaving them potentially in a worse legal position than they are today.
Underlining the difficulty of the task confronting May, The Sunday Telegraph reported the prime minister will face an immediate leadership challenge from eurosceptic lawmakers in her party if she seeks to water down her plans for Brexit.
The minister added: We want both sides to emerge strong and prosperous, capable of projecting our shared European values, leading in the world, and demonstrating our resolve to protect the security of our citizens.