Shadow Chancellor John McDonnell it was “message received” with mid-morning results showing Labour facing a net loss of several dozen councillors and two councils overall.
And responding to the early results, Labour Party chairman Ian Lavery said: “'We've got a clear message from a lot of these communities that the two main parties need to get on and get Brexit sorted”.
But that message was resisted by pro-Remain figures in Labour still fighting for a second EU referendum, who pointed to big gains by the Liberal Democrats and Greens.
“Delivering a Brexit that will damage the lives of working people across our country would be a mistake of catastrophic proportions.”
Talks between Labour and the Conservatives on a Brexit compromise deal will reach their climax next week, with time set aside for votes in the Commons on a possible agreement.
The government says the discussions must conclude by the middle of next week if European elections on 23 May are to be avoided.
In Sunderland, which voted to leave the EU by 61%, Labour held on to the council but lost twelve wards, with the Liberal Democrats, Greens, Ukip and Tories all making gains.
The council leader said the losses were down to Labour MPs calling for a People’s Vote.
And in the Labour heartland of Bolsover, the party lost control of the council for the first time, with independents making the biggest gains.
Mr McDonnell posted on twitter: "We'll see what final results of local elections look like by end of day as they are pretty mixed geographically up to now but so far message from local elections - 'Brexit - sort it'. Message received."
Responding to the Shadow Chancellor’s message, First Minister Nicola Sturgeon replied on social media: "If the message Labour takes from English local elections is that they should now be the facilitator of a Tory Brexit, I suspect their troubles will just be beginning."
As the polls closed, Labour shadow cabinet member Barry Gardiner was involved in an angry exchange with the Conservative Party deputy chairman James Cleverley, telling him Labour were “bailing out” the government in Brexit talks.
The prompted an immediate reaction from Labour MP Wes Streeting, who insisted: "Any deal - any - must go to a public vote. Without a commitment to a public vote, I'll vote for a Labour-Tory deal when hell freezes over and I'm not alone in that."
Jeremy Corbyn, on a visit to Trafford, a former Tory stronghold where Labour won over-control of the council, said: “Our policy is that we're the only party that seeks to appeal to people however they voted in 2016".
Mr Corbyn said: "Results across the country are interesting, to put it mildly.
"But I also say the swings to Labour in many parts of the country show that we can win seats in a general election, whenever that comes.
"And I'm very pleased with the result here. I'm very pleased with the result just down the road in Telford, where there's been a huge swing to Labour. Seats have been gained there, as seats have been gained in many parts of the south as well as various parts of the north.
Scottish Tory leader Ruth Davidson, who begins her party’s conference in Aberdeen today, told Sky News: "I think the message is pretty clear. It seems to be a plague on both your houses to the Conservatives and the Labour Party, who they see as a block on finding some sort of resolution to Brexit.
"So, we know that the talks are ongoing; hopefully, this will focus minds in the room and, hopefully, we can get past the impasse that we are in and move on to the next stage."
Theresa May is set to address Scottish Tories in Aberdeen this afternoon.