Labour has blamed “unique circumstances” for what the party predicted would be a “challenging” set of results in local and mayoral elections on Thursday. The polls held across England, Scotland and Wales come just five weeks before the surprise general election called for 8 June by the prime minister, Theresa May.

Jeremy Corbyn’s team played down expectations of their party’s performance, accepting that Labour could be set to lose hundreds of council seats, particularly in Scotland and Wales.

Labour said that when these council seats were last contested, there was a strong performance for the party, then led by Ed Miliband. “These elections are a challenging set of contests held in unique circumstances,” a Labour spokesman said. “They’re individual contests being fought in very differing situations, from local council-level issue-driven campaigns up to large mayoral fights with some well-known politicians.

“Nonetheless, Labour has been making the case up and down the country that Labour representatives, both locally and nationally, will stand up for the many whilst the Conservative party stands up only for the few. That’s what we’ll be doing all the way through to 8 June and we are confident that will start to resonate as we get closer to that date.”

In total, 35 English council elections – most of them county councils – and every seat in Scotland and Wales were up for grabs.

Turnout generally had been “slow but steady,” John Turner, chief executive of the Association of Electoral Administrators, told the Local Government Chronicle.

The first handful of results looked grim for Labour, with the party losing seats to the Conservatives in Wrexham, north Wales, with large swings, and in Harlow, Essex.

As the counts began in Wales, the shadow Welsh secretary, Christina Rees, thanked Welsh Labour candidates and hinted at a difficult night ahead, saying: “It always inspires me that even when times seem tough for Labour, they never fail to rise to the challenge with a passion and energy that no other party can match.”

Strategists from all the major parties will be scrutinising the results closely for signs that May’s relentless message of providing “strong and stable leadership” has persuaded habitual Labour voters to defect to the Conservatives. The local elections will also provide the first real test of the hypothesis that Ukip’s vote is collapsing in the Tories’ favour, as May pledges to deliver Brexit.

Labour sources suggested the overall picture was complex and only the national vote share would be an indication of what may be to come in the general election. But losses in traditionally Labour areas where the local MP has a small majority will inevitably raise fears that the party is on course for a heavy defeat next month.

Anthony Wells of pollsters YouGov pointed out that the Labour party was just three percentage points behind Margaret Thatcher’s Conservatives in the 1983 local elections, but trailed by 16 percentage points in the general election that followed just a month later.

Wells said: “Don’t just assume that the projected overall shares of the vote at this week’s votes are going to be repeated in next month’s election. People vote differently for different reasons at different sorts of election.”

That picture – of voters backing Labour locally but peeling away in a general election – was acknowledged by Susan Woodward, the leader of the Labour group on Staffordshire county council, where elections were held on Thursday.

Woodward said she felt positive, but admitted that some voters had promised to back the party in local elections but not on 8 June. “I’m hoping that having good, strong community leaders overrides any national swings – that is what I’m hoping for me and my Labour colleagues,” she said.

“If people are saying, ‘I will vote Labour in locals but not in general’ – and we’ve had a sprinkling of those – the leadership have to listen and redouble their efforts. They need to show they are focusing on Labour voters’ priorities rather than their own priorities.”

In Scotland, Labour controls or shares power in 18 of the country’s 32 unitary councils, including its bastion of Glasgow, plus a swath of largely urban authorities in central and western Scotland and the capital city, Edinburgh. The polls suggest it could lose power in most, if not all, of those to the Scottish National party and potentially to the Tories – at best clinging on by forging coalition deals with other parties.

As well as local councillors in England, Scotland and Wales, voters were choosing six new English regional mayors, as part of a wave of devolution set in train by former chancellor George Osborne.

Former MPs Andy Burnham and Steve Rotheram are expected to win Manchester and Liverpool respectively for Labour, but the West Midlands race appeared too close to call on Thursday night.

In a sign of the Conservatives’ confidence, May was pictured calling West Midlands voters to urge them to back her candidate, former John Lewis boss Andy Street, against Labour’s Siôn Simon.

If the Conservatives can clinch the West Midlands mayoralty, which covers seven local authority areas including Birmingham, Coventry and Wolverhampton, it will provide a powerful boost for May’s hopes of penetrating deep into Labour territory in the general election. Labour holds 301 council seats across the local authorities covered by the new West Midlands role, against the Conservatives’ 139.

Counting will not start until Friday morning, but Street, whose campaign has been boosted by a series of high-profile ministerial visits, including from Boris Johnson, said he believed the race was “neck and neck”. He said he had received backing from habitual Labour voters with doubts about the party and also from swing voters.

“We see a lot of non-committed voters, who say: ‘I’m going to vote for you this time, because they admire how the prime minister is heading,” he said. “Or they say: ‘I want someone for the West Midlands who has experience, who can get things done.’”

The only woman likely to win one of the six new mayoralties is Labour’s Sue Jeffries, who is odds-on to win in Tees Valley, a Labour-voting region of north-east England that includes Middlesbrough, Hartlepool and Darlington. Turnout, however, is predicted to be dismally low, perhaps less than 20%.