Labour risked a damaging split over Brexit as Jeremy Corbyn faced calls to back keeping the UK in the single market.
The party hierarchy was accused of "cowardice" and adopting a "ridiculous" position by telling peers not to support a call for the Government to negotiate a Norway-style Brexit within the European Economic Area (EEA).
But shadow international trade secretary Barry Gardiner said such an arrangement would reduce the UK to being a "rule taker" without a seat at the table when decisions on regulations are made.
And shadow chancellor John McDonnell insisted the party must promise a "traditional British compromise" balancing the interests of Leave and Remain voters.
Pro-EU Labour parliamentarians have reacted with fury over the party's refusal to support a Lords amendment which would require the Government to negotiate EEA membership.
Labour's Lord Alli, one of the signatories to the amendment, accused the party leadership of being "paralysed by indecision".
He told The Observer: "This is complete cowardice. There is no point in being in politics to abstain, if you stand in the middle of the road someone is going to knock you over."
Former shadow cabinet minister Chuka Umunna lashed out at the stance, adding: "Most of our members, supporters and voters think we should vote for the EEA."
Ex-shadow chancellor Chris Leslie hit out at Mr Gardiner, saying if he blocked the EEA vote he would share responsibility for "hard Brexit, job losses and (a) fall in tax revenues" and would be left with "zero credibility" to complain about austerity.
But Mr Gardiner, who has said the EEA model would leave the UK a "vassal state" of the EU, told the BBC's Sunday Politics: "The EEA option would actually have less control, we would be bound by the regulations but we would have no seat at the table in deciding what those regulations were."
He added: "We should not vote for a substantive amendment that talks about staying in the EEA."
Labour MPs were whipped to back a call to keep the UK in the EEA when the EU (Withdrawal) Bill went through the Commons and Mr Umunna said Lord Alli's amendment was consistent with that.
"Labour MPs were whipped to vote in the Commons for it and yet now, when there are enough Tory rebels, we abstain - this is ridiculous," he said.
But Mr Gardiner told ITV's Peston On Sunday "I don't believe we have changed" position.
Mr McDonnell told BBC1's Andrew Marr Show: "What people want is a traditional British compromise.
"Respect the referendum result, but get the best deal you can to protect our economy and protect our jobs."
That meant being in "a customs union" and remaining "close to the single market".
Meanwhile former Europe minister Caroline Flint called for Labour colleagues to accept Brexit is happening and said the "parliamentary games" must stop.
"If Labour fails to stand by the 2016 vote, we risk alienating many traditional Labour voters," she said.
"We should all heed the warning from Thursday's local elections."