Polls have opened for council and mayoral elections across England and Northern Ireland, with the Conservatives predicted to suffer significant losses to the Liberal Democrats and Labour.

More than 8,000 seats are up for grabs on 248 English councils and all 11 Northern Irish councils, plus six mayoral posts. No elections are taking place in Scotland, Wales or London.

The Tory peer Robert Hayward, a leading polling analyst, has said the Conservatives can expect to lose 800 or more seats as voters punish Theresa May’s administration for the Brexit impasse. Conservative campaigners were encouraged to pursue a “bins not Brexit” approach to doorstep campaigning.

The Lib Dems are the most likely to benefit, and though some support will come from their unequivocal position on Brexit, another factor is likely to be the party making up ground after catastrophic losses in 2015.

Hayward predicted the Conservatives could lose about 500 seats to the Lib Dems and 300 to Labour. The latter traditionally makes fewer gains in the shires, where many of the elections are being held.

Several Labour sources have suggested the Tories have exaggerated the extent of their expected drubbing in order to manage expectations, but a bad night for the Conservatives is likely to foreshadow punishing results in the European elections, which are likely to take place on 23 May if the government cannot pass a Brexit deal before polling day.

Two new parties, the pro-remain Change UK and the Brexit party, led by Nigel Farage, are not standing in the local elections.

Chuka Umunna, the former Labour MP who is Change UK’s spokesman, said voters should pick remain parties such as the Lib Dems or the Greens in order to send a message to the Tories and Labour. His party has rejected entreaties to strike any deal with those parties for the EU elections, suggesting it would not be permitted by EU law.

More than 100 English councils will count their results overnight and are expected to declare before 6am on Friday, with the remaining 140 results scheduled to come in throughout Friday. Northern Ireland councils are expecting to take longer.

Voters in 10 local authorities, including Braintree, Derby, Woking and Pendle, are required to bring a form of ID, an initiative that has been criticised by pro-democracy groups for having the potential to deter turnout.