Tories and Labour braced for bad night at the polls: here's why
The Liberal Democrats, from the opposite side of the Brexit divide, are also expected to pick up votes.
The European elections took place almost three years after the UK voted to leave the EU because of Theresa May's failure to get her Brexit deal through Parliament, and could deliver a damaging blow for the Tories after a distinctly lacklustre campaign.
Prominent Conservative MEP Daniel Hannan said he feared the party was facing "total wipeout" and would be left without any representation at all.
The Brexiteer, who has been a member for South East England since 1999, said he suspected the party would be left with "zero MEPs" following the poll.
Seventy-three MEPs will be elected to represent the UK, with England, Scotland and Wales using a form of proportional representation called the D'Hondt system and Northern Ireland using the single transferable vote method.
Mr Farage, who is standing in the South East constituency, said: "If you want Brexit, you've got to vote Brexit. We did it once, they ignored us, so we're going to tell them again."
In a polling day video message, Mr Corbyn warned "the far right is on the rise" and Britain was "at a crossroads".
"The actions we take now will have huge consequences for our future," he said.
On a campaign visit to Worthing, he added: "This Government can't last very long. And so, get ready for a general election."
But in a sign of Labour's divisions over Brexit, pro-EU MPs Wes Streeting and Ben Bradshaw both spoke of difficult doorstep experiences.
Former Cabinet minister Mr Bradshaw said it was a "dispiriting" experience to see Labour voters "flocking" to the Remain-supporting Greens and Lib Dems, while Mr Streeting said it was "not the easiest of polling days".
Writing in The Observer, deputy Labour leader Tom Watson said the party was "braced with a sense of despair" and blamed Labour's ambiguous position on a second Brexit referendum for losing votes.
"I want reports of high turnout in Remain areas to reflect a huge gain in votes for Labour. I fear that won't be the case," he said.
In Ireland, an exit poll has indicated the Green Party could top the European election in Dublin.
The increased support looks widespread, even accounting for a 4% margin of error, and could see an unexpected boost in Ireland's two other constituencies, RTE said after commissioning a RedC exit poll.
Thirteen MEPs are being elected in Ireland, but two will face an uncertain wait as to when they can actually take their European Parliament seats.
The country is getting two of the 27 seats formerly reserved for the UK that are being redistributed among 14 member states as a result of Brexit.
The problem for the duo elected in last place in the Dublin and South constituencies is Brexit has not happened and does not look like happening any time soon, and British MEPs are set to attend the inaugural plenary session of the new parliament on July 2.
Results of the elections will be announced after 10pm on Sunday, when the final polls have closed across Europe.
The turnout figure covering Birmingham was down slightly on the European elections in 2014 at 31.1% (32.4% in 2014).
And the turnout for the South East in the European elections is 39.36% which is up from 36.3% in 2014.
Turnout in the North West was 33.1%, which was marginally down from 33.3% in 2014.