The leaflet pledges that the party will deliver Brexit by seeking "a better deal with Europe" but does not mention its policy of supporting another public vote on any exit deal approved by parliament.
MPs said the leaflet had caused "complete meltdown", with supporters of a Final Say vote "utterly furious" at what they suggested was an attempt by Labour staff to undermine the party's policy.
Jeremy Corbyn's top team is deeply divided on the issue of a second referendum. Senior shadow ministers including shadow Brexit secretary Sir Keir Starmer, deputy leader Tom Watson and shadow foreign secretary Emily Thornberry back another referendum despite strong opposition from others, including party chairman Ian Lavery, shadow Cabinet Office minister Jon Trickett and some of Mr Corbyn's closest advisers.
Sir Keir and Ms Thornberry have said that the party supports a "confirmatory vote" on any Brexit deal approved by MPs, while Mr Corbyn's team insists Labour would back a referendum only on the government's deal or to avoid a no-deal exit.
The leaflets, which were passed to The Independent, do not mention any referendum.
Under the heading "a better deal with Europe", they say only: "The Tories' chaotic handling of Brexit has left our country in crisis.
"With Labour, Britain will have a proper say in future trade deals and businesses wouldn't have to pay to trade with Europe.
"Labour will keep a close relationship with the EU and protect workers' rights."
It is understood that neither shadow cabinet ministers nor Labour MEPs had signed off the leaflet, which was drawn up by Mr Corbyn's team and staff at Labour's HQ.
Sources said many MPs were furious when they saw they draft leaflet.
One Labour MP told The Independent: "People went into complete meltdown and were utterly furious at what appears to be yet another attempt by a small cabal of disgruntled officials to undermine the entire rest of the party, with no reference to the very candidates these leaflets are meant to promote."
They added: "It's quite extraordinary to see this early draft of a leaflet which makes no mention of Labour's key conference policy on Brexit, especially just a day after the international commission [of Labour's National Policy Forum] responsible for drawing up our policy on these issues unanimously supported a confirmatory vote.
"I sincerely hope this is an early draft because it would be unacceptable for unelected officials to attempt to subvert Labour's members, trade unions and elected representatives in this way."
Michael Chessum, national organiser for grassroots Labour group Another Europe is Possible, said: "Labour cannot go into these elections with anything less than a clear commitment to public vote and a transformative vision for Europe. This is an election about Brexit, and about the future of Europe, in which Labour's main opponents are literally called the Brexit Party.
"The current draft of the leaflets is less head in the sand than head smacking repeatedly and pointlessly into a concrete pavement. It's not even radical on domestic policy. Nigel Farage would be delighted if these went out, and party activists and supporters demoralised. Hopefully there will be time to rethink."
A Labour spokesperson said: "This is a short pre-manifesto leaflet to introduce our candidates and set out our commitment to Leave and Remain voters to bring our country together.
“It highlights how the Tories’ chaotic handling of Brexit has left our country in crisis and how our MEPs will fight for proper investment in communities, housing, jobs and industries. Our full manifesto, which will address the issues of a Brexit deal and the circumstances of a referendum, will be published after the local elections."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies