The Liberal Democrats appear to have suffered their worst performance at the polls in 30 years, suffering heavy losses across the north of England, Scotland and Wales.

Nick Clegg admitted his party was taking the brunt of the blame for a perception that the coalition government is dragging Britain back to the Thatcherism of the 1980s.

The Lib Dem leader and deputy prime minister said the party had taken "big knocks" in the local elections.

"Clearly what happened last night – especially in those parts of the country, Scotland, Wales, the great cities of the north, where there are real anxieties about the deficit reduction plans we are having to put in place ... we are clearly getting the brunt of the blame," he told reporters.

"To the many families, in those parts of the country especially, there are some very strong memories of what life was like under the Thatcherism of the 1980s, and that's what they fear they are returning to. We need to get up, dust ourselves down and move on."

The Labour leader, Ed Miliband, later said: "North, south, east and west, Labour is making gains and coming back. I say this to David Cameron and Nick Clegg this morning: you must listen to the people.

"The Conservative party does not have a majority in parliament and has only been able to govern because of the Liberal Democrats' willing participation in a Tory-led government. People who once voted Liberal Democrat have yesterday withdrawn permission for Nick Clegg to back Tory policies on the NHS, on living standards and cuts that go too far, too fast.

"People do not want a relaunch of the coalition but real change. David Cameron and Nick Clegg must listen to the people."

Ministers insisted the Lib Dem-Tory government would refocus on its work – next week Clegg and Cameron will launch a new coalition document marking achievements in the year since it was formed – but recriminations over the Liberal Democrats' drubbing, and in anticipation of a humiliating defeat in the AV referendum, have already begun.

The former Lib Dem leader Paddy Ashdown told the Guardian the days when the coalition was "lubricated by a large element of goodwill and trust" were gone.

The party has lost swaths of seats in English councils, the Welsh assembly and four out of the six seats in the Scottish parliament declared so far.

The Lib Dems lost control of Sheffield council – the city of Clegg's constituency – were ousted from Liverpool, Hull and Stockport, and lost every Manchester seat the party stood in. Overall, it got its lowest share of the vote in three decades.

Danny Alexander, Lib Dem MP and chief secretary to the Treasury, said: "This is, of course, the first time the Liberal Democrats have had the experience of being in government in Westminster.

"It tends to be the case that parties in government tend to lose ground in local elections ... given the difficult decisions we've had to make, some voters have decided to vote for others."

Paul Scriven, the Liberal Democrat leader of Sheffield council, said: "Maybe in three or four years time, people will look back and say they were a little bit harsh to the Liberal Democrats."

Labour was celebrating a resurgence in English local elections, retaking the northern cities they lost after the Iraq war and during the most unpopular days of the Labour government.

Symbolically, the party also made important inroads into the south, winning Gravesham, while the Lib Dems lost control of Bristol as Labour gained.

But even the party's gains in the Welsh assembly, at the expense of Plaid Cymru, could not ease the pain of the losses in Scotland, where the Scottish National party has had spectacular success with 48 seats so far.

The BBC is reporting that the SNP could take control of the Scottish parliament once the second stage of counting, a proportional list vote, is completed.

Michael Moore, the Lib Dem Scotland secretary, told the BBC: "I am not going to duck the fact that this is a very, very disappointing evening for us in Scotland and around the country as well.

"We have been involved in taking some very tough decisions over the course of this parliament. This is a difficult moment for some of our colleagues to be standing for election.

"The big story in Scotland is how on earth the Labour party lost what was a massive lead in the opinion polls and are now losing some of their most able frontbenchers in seat after seat across central Scotland. It is a very good night for the SNP."

But the surprise of the night was the resilience of the Tory vote, with the party winning two additional councils, including Ryedale, so far.

Tony Travers, the professor of local government at London School of Economics, suggested a hardening of the two-party divide in England now the Liberal Democrats are no longer the "protest vote" against the major parties.

Downing Street is hoping to put the coalition back on track next week with the publication of the document detailing its achievements.

Oliver Letwin, the cabinet's policy guru, will relaunch the departmental business plans refocusing each department's aims.

But the coalition must first get over its most bitter divide when the AV referendum result is likely to bring a painful end to what has been a desperate week for the Lib Dems.

Even before the first election results had come in – and before the AV referendum count had begun – the recriminations had started.

Ashdown launched a ferocious attack, made after consultations within the party, saying the "rose garden days" of the coalition were over.

He told the Guardian: "So far, the coalition has been lubricated by a large element of goodwill and trust. It is not any longer.

"The consequence is that, when it comes to the bonhomie of the Downing Street rose garden, that has gone. It will never again be glad confident morning."

On Friday morning, he went further, telling the BBC that the Tories' handling of the No vote in the AV campaign had been "bloody stupid".

"If you are the Conservative party and if you fund a campaign against AV that trashes your coalition partner and then hand that campaign over to the Labour party to run, then I don't put that in the box marked betrayal, I put it in the box marked bloody stupid," he said.

Ashdown is furious with the no campaign for personal attacks on Clegg that accused the deputy prime minister of broken promises on tuition fees and spending cuts and arguments that AV was a "Lib Dem fix".

Ashdown said: "The bottom line is that Liberal Democrats are exceedingly angry. We believe there has been a breach of faith here.

"If the Conservative party funds to the level of 99% a campaign whose central theme is to denigrate and destroy our leader, there are consequences for that.

"What that means is that this is a relationship that is much less about congeniality, it becomes a business relationship, a transactional relationship, and maybe it will be all the better for that."

He added: "David Cameron is the prime minister. He sets the tone of politics in this country. It is an unhappy fact that when he was asked to dissociate himself from a campaign that was run on the basis of personalisation and personal attacks, and messages that were far more than some subtle bending of the truth, he refused to do that."

Ashdown also accused Cameron of panicking after demands from Tory backbenchers to step up the referendum campaign.

"In backtracking, to use no stronger a word than that, on what was a private agreement he had with Nick Clegg about the way this campaign was conducted, I think the prime minister panicked in the face of his rightwingers. I regret that.