The Daily Express runs with the headline: "Outcry at Labour's betrayal of Brexit", and says the Labour leader faced a "furious backlash" after confirming he was ready to join calls for a re-run of the 2016 poll if delegates back the demand in a vote at the party's conference.
Most of the party's half a million members voted in 2016 to remain in the European Union, but many of its 257 lawmakers represent areas that supported Brexit.
But, speaking at a fringe meeting at Labour's conference in Liverpool, Mr Gardiner said it was time to "inject some realism into the debate".
Later, asked directly what options should be part of a second referendum question, he said: "My view at the moment is that parliament will decide what will be on that ballot paper".
"We argued for "Remain" in the past but we lost that vote so we have to respect that", he told the BBC.
Labour leader Jeremy Corbyn said over the weekend that he would shift his weight behind a decision to stage another Brexit referendum, should his party demonstrate clear support for the move.
On ITV1's Good Morning Britain, Mr McDonnell suggested that a general election would be "the real People's Vote" because it would give the public the chance to change the team carrying out the negotiations, replacing Theresa May with a Labour government.
"I tell you what: they are on borrowed time because a Labour government is coming".
When challenged that he was scaremongering, Mr Lloyd pointed to comments from PSNI Chief Constable George Hamilton, who said that the Border would be a target for paramilitaries in the event of a hard Brexit.
Labour could play a deciding role in whether any Brexit deal is approved by parliament.
Andrew Adonis, a Labour member of the House of Lords who supports holding a second referendum, said Labour can't sit on the sidelines while the country staggers toward political and financial chaos.
"But when Theresa May comes back with a supposed deal, we'll see what she comes back with, we'll put it against the tests we have advocated, the main test is about protecting jobs and the economy".
Stoke-on-Trent Central MP Gareth Snell said: "I don't support a second referendum, I don't support a People's Vote. That was clearly the mood of the room, and in fact that's reflected in the motion".
But he has also claimed they are being forced out the party by supporters of Mr Corbyn - something denied by Mr Corbyn.
"If we can't get a general election, we've kept the option of People's Vote on the table and that's what we'll go for, but I'd much prefer a general election".
"The leadership knows where the members are and they know where their voters are".
In a fiery response to the bloc's "unacceptable" attitude, Mrs May warned she would sooner leave without a withdrawal agreement rather than accept a "bad deal". "It will make the 2016 referendum look like a walk in the park".