Results are not expected to be announced until Sunday evening, after the last polling station on the continent closes.
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Theresa May and Jeremy Corbyn are expected to face a drubbing as Britain heads to the polls for the European elections on Thursday.
The Conservative and Labour parties are predicted to suffer severe losses, with the Liberal Democrats and the Brexit Party likely to hoover up votes.
Seventy three MEPs will be elected to represent the UK, using a form of proportional representation called the D’Hondt system.
Results will not be announced until Sunday evening when the last polling station on the continent closes.
England is split into nine regions: South East England has 10 MEPs, London and North West England each have eight, East of England and the West Midlands each have seven, Yorkshire and the Humber and South West England have six each, the East Midlands has five and North East England has three.
Scotland has six MEPs, Wales four and Northern Ireland three.
Mrs May had hoped cross-party Brexit talks would deliver a compromise deal in time to allow her to call off the European Parliament elections.
But, more than a month after the talks began, her de facto deputy David Lidington acknowledged time was too tight to get a Withdrawal Agreement Bill through both Houses of Parliament by the date of the poll.
Downing Street conceded on Wednesday that they expected a “very challenging night” when the results come through.
A spokesman said: “The PM is focused on the task at hand which is delivering the Brexit people voted for.”
Labour leader Jeremy Corbyn said voting for Labour represented a vote for a “tolerant and fairer country”, and an “end to the division and austerity which has devastated our communities for a decade”.
He said: “The threat from the far-right is real. They serve only to sow division and offer no solutions. A vote for Labour today will challenge the far-right in Britain and across Europe.
“A vote for Labour is a vote to bring our divided country together, whether you supported Remain or Leave. We are the only party working for a sensible solution to break the Brexit deadlock and protect jobs, rights and living standards.
“We will continue to oppose the Tories’ bad deal or a disastrous No Deal. If we can’t get an agreement along the lines of our alternative plan, we will take it back to the people whether it’s through a public vote or general election.
“A vote for Labour is a vote for the only party that stands for the real change our country desperately needs, to benefit all communities, not just a privileged few.”
When Britain does finally leave the EU, the European Parliament will reduce from 751 MEPs to 705, with 27 of the UK’s 73 seats being distributed among the remaining member states.
Harriet Line is Press Association Political Correspondent.