The Brexit Party was the clear winner in the UK's European elections، with the pro-EU Lib Dems coming second، according to BBC.
The Conservatives and Labour suffered heavy losses، with the former expected to get less than 10% of the vote.
Brexit Party leader Nigel Farage said he was ready to "take on" the Tories and Labour in a general election.
Overall، out of 64 MEPs declared so far، Mr Farage's party has won 28، the Lib Dems 15، Labour 10، Greens seven، the Tories three and Plaid Cymru one.
Mr Farage told BBC Radio 4's Today programme: "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."
The deputy leader of the pro-Remain Liberal Democrats، Jo Swinson، said the result should "give hope to all of the people out of there who want to stop Brexit"، and that they "should not be giving up without a fight".
"When there is such a general shambles over Brexit، then [a further referendum] is the best way out of the impasse،" she told Today.
Polling expert Sir John Curtice said the results showed just how polarised the country had become.
All 28 EU member states are electing MEPs to the European Parliament - the EU's law-making body. Overall، the big centre-right and centre-left blocs lost ground، amid a surge in support for liberals، Greens and nationalists.
The UK had been due to leave the EU on 29 March، but when that deadline was missed، participation in the election became mandatory.
The Brexit Party topped the polls in every region of England apart from London. It also dominated in Wales، with Plaid Cymru second.
It has now become the joint largest national party in the European Parliament، alongside Germany's CDUCSU party.
Scotland is yet to formally declare، but with most votes counted، the SNP is on course for a resounding victory، with about 38% of the vote.
Meanwhile، Northern Ireland's count does not begin until Monday، with the results expected on Tuesday.