However, the Conservatives and Labour suffered heavy losses, with the former expected to get less than 10 percent of the vote.
Farage, the Brexit Party leader, said he was ready to "take on" the Tories and Labour in a general election.
Farage’s success campaigning in favour of a no-deal Brexit is, according to pundits, likely to push the Conservative leadership candidates into hardline positions on leaving the EU.
Boris Johnson, an early frontrunner to succeed Theresa May as UK Prime Minister, has already warned that under his leadership the UK will leave the EU on 31 October “with or without a deal.”
The Brexit party, in Sunday’s elections, exceeded expectations after it gained 28 seats, with the Liberal Democrats in second place with 15 seats.
Labour held 10, having lost seven, the Green party won seven, a gain of four, and the Conservatives were languishing in fifth place, with just three seats.
The Brexit party, formed by former UKIP leader Farage only six weeks ago, won all of the regions in England, apart from London, as well as Wales, and took almost 2 million more votes than their closest rivals, the Liberal Democrats.
“This was a spectacular success and, believe me, this is only the start of things to come” Bill Etheridge MEP
UK MEP Bill Etheridge, formerly of UKIP, who joined the Brexit party soon after it was formed, told this website, “This was a spectacular success and, believe me, this is only the start of things to come.”
UKIP, which dominated the headlines in the last elections five years ago, was virtually wiped out this time.
Among those elected to the European parliament for the Brexit party were the former Conservative MP Ann Widdecombe and Annunziata Rees-Mogg, the sister of the Conservative hard Brexiter Jacob Rees-Mogg.
The Brexit Party chair Richard Tice won a seat in the East of England.
Among the Conservatives casualties in the EU-wide poll was the party’s European Parliament leader Ashley Fox.
The prominent Tory Brexiter MEP Daniel Hannan, one of the key figures in Vote Leave, was narrowly re-elected.
“It’s been a very bad night and, in a way, understandably; you don’t need to be any kind of expert on politics - people voted leave and we haven’t left” Daniel Hannan MEP
Hannan said it was “the worst result my party has suffered in its 185-year history” adding, “It’s been a very bad night and, in a way, understandably; you don’t need to be any kind of expert on politics - people voted leave and we haven’t left.”
The results so far show that the hard Brexit vote totalled 34.9 percent - with the Brexit party on 31.6 percent and UKIP on 3.3 percent.
The overall total for pro-leave parties was up at 44 percent, including the Conservatives at a historically low 9.1 percent.
The pro-remain vote added up to 40.3 percent - with the Lib Dems at 20.3 percent, the Greens at 12.1 percent, the SNP at 3.5 percent, Change UK at 3.4 percent and Plaid Cymru at 1 percent.
Labour, which tried to appeal to both sides with a soft Brexit pitch or a possible confirmatory referendum, was at 14.1 percent.
In Wales, Plaid Cymru took the lion’s share of the pro-remain vote, but the Brexit party topped the poll, snatching a seat from the Conservatives and one from UKIP.
In Scotland, where the final result will not be known until later on Monday, the Scottish National party was predicted to win three MEPs, with Labour failing to win a single seat.
“There’s a huge message here, massive message here. The Labour and Conservative parties could learn a big lesson from tonight, though I don’t suppose that they actually will” Nigel Farage, Brexit Party
The night also saw a significant boost for the Green party, a pattern seen in other parts of Europe.
Molly Scott-Cato, the Green MEP re-elected in the South West, said it was a “thrilling night” for Greens across Member States.
Farage, re-elected to Parliament in the south east of England, was understandably jubilant, saying, "With a big, simple message - which is we've been badly let down by two parties who have broken their promises - we have topped the poll in a fairly dramatic style.”
“The two-party system now serves nothing but itself. I think they are an obstruction to the modernising of politics... and we are going to take them on."
“Never before in British politics has a new party launched just six weeks ago topped the polls in a national election. There’s a huge message here, massive message here. The Labour and Conservative parties could learn a big lesson from tonight, though I don’t suppose that they actually will.”
Further reaction to the results came from UK Labour leader Jeremy Corbyn who said: “After three years of Tory failure to deliver a Brexit that works for the whole country, these elections became a proxy second referendum.”
“Over the coming days we will have conversations across our party and movement, and reflect on these results on both sides of the Brexit divide,” he added.
The outgoing Liberal Democrats leader Vince Cable said voters had backed its “clear, honest, unambiguous message” and delivered the party’s best European elections result, which means they have more MEPs than MPs in the House of Commons.
“There is a clear lesson for Labour in tonight’s results: get off the fence. In trying to please everybody they have pleased nobody,” said Cable, who is due to stand down as leader next month.