The UK Independence Party is a truly national force and has "momentum" behind it, Nigel Farage has said after its victory in the European elections.
Hailing a "breakthrough" in Scotland and a strong showing in Wales, he said UKIP would target its first Westminster seat in next week's Newark by-election.
Lib Dem leader Nick Clegg has said he will not resign after his party lost all but one of its 12 MEPs.
He said he was not going to "walk away" from the job despite the poor results.
Mr Farage has been celebrating his party's triumph in the European polls, the first time a party other than the Conservatives or Labour has won a national election for 100 years.
UKIP won 27.5% of the vote and had 24 MEPs elected. Labour, on 25.4%, has narrowly beaten the Tories into third place while the Lib Dems lost all but one of their seats and came sixth behind the Greens.
With Northern Ireland yet to declare its results, the election highlights so far have been:
- Far-right, anti-EU parties, including the Front National in France, made gains across Europe, as did anti-austerity groups from the left
- Labour has 20 MEPs so far, an increase of seven on 2009, which was a record low point for the party
- It topped the poll in Wales by a narrow margin from UKIP. The SNP won two seats in Scotland, where UKIP also won its first MEP
- The Conservatives have so far secured 24% of the vote nationally and lost seven seats
- The Lib Dems slumped to fifth place
- The Green Party came fourth and has got three MEPs - one more than it achieved in 2009. BNP leader Nick Griffin lost his seat as the party was wiped out, the English Democrats also saw their vote share fall
- Coverage is on the BBC News Channel and BBC World. You can follow all the latest news, reaction and results on bbc.co.uk/vote2014
Mr Farage has said his party intends to build on what he has described as "the most extraordinary result" in British politics in the past century.
Speaking in London at an election rally, he said his party now appealed to all social classes and had made significant inroads in Wales and Scotland as well as winning the most votes in England.
He said the party was aiming to win the Newark by-election next week, to try and "turn the heat" up on David Cameron. They would target a dozen or more seats in next year's general election, he added.
"Our game is to get this right, to find the right candidates, and focus our resources on getting a good number of seats in Westminster next year.
"If UKIP do hold the balance of power, then indeed there will be a (EU) referendum."
Mr Farage said Labour would come under "enormous pressure" to offer the voters a referendum on Europe, and he said he did not believe Nick Clegg would still be Lib Dem leader at the general election.
"The three party leaders are like goldfish that have been tipped out of their bowl onto the floor and are gasping for air," he said.
Mr Clegg is facing calls to stand down after Sunday night's results, with MP John Pugh saying the "abysmal" performance meant the Lib Dem leader should make way for Vince Cable.
But Mr Clegg said he had no intention of stepping down despite the "gut-wrenching" loss of most of the party's representatives in Brussels.
"Of course it's right to have searching questions after such a bad set of results," he said.
"But the easiest thing in politics when the going gets really really tough is to wash your hands of it and walk away, but I'm not going to do that and neither is my party."
Lib Dem Business Secretary Vince Cable added: "These were exceptionally disappointing results for the party. Many hard-working Liberal Democrats, who gave this fight everything they had and then lost their seats, are feeling frustrated and disheartened and we all understand that."
Mr Clegg "deserves tremendous credit" for having been bold enough to stand up to "the Eurosceptic wave which has engulfed much of continental Europe", he said.
The party had taken a "kicking for being in government with the Conservatives", but must now "hold its nerve", he said.
"Now is not the time for infighting and introspection," he said. "There is no leadership issue."
Reacting to his third place, David Cameron said the public was "disillusioned" with the EU and their message had been "received and understood", but he rejected calls to bring forward his proposed in/out EU referendum to 2016.
After UKIP's success, the Tory leadership is facing renewed calls for an electoral pact with their rivals to avoid a split in the right of British politics at next year's general election.
Daniel Hannan, who was returned as a Tory MEP in the South East region, said it would be "sad" if the two parties "were not able to find some way, at least in marginal seats, of reaching an accommodation so that anti-referendum candidates don't get in with a minority of votes".
But Mr Cameron said it was a "myth" that the two parties had a shared agenda.
Labour was looking at one stage as if it might be beaten into third place by the Tories - a potentially disastrous result for Ed Miliband as he seeks to show he can win next year's general election.
But the party was rescued by another strong showing in London - and it took heart from local election results in battleground seats, which party spokesmen suggested were a better guide to general election performance.
Mr Miliband said the party was "making progress" but had "further to go" if it was to prevail in next year's general election.
He said the outcome of the elections was about more than Europe and his party must respond to a "desire for change" over a wide range of issues.
BNP leader Nick Griffin lost his seat and saw his party's vote collapse by 6% in the North West of England.
Anti-EU parties from the left and right have gained significant numbers of MEPs across all 28 member states in the wake of the eurozone crisis and severe financial squeeze.
However, pro-EU parties will still hold the majority in parliament.
Turnout across the EU is up slightly at 43.1%, according to estimates. Turnout in the UK was 33.8%, down slightly on last time.
In the European elections five years ago, the Conservatives got 27.7% of the total vote, ahead of UKIP on 16.5%, Labour on 15.7%, the Lib Dems on 13.7%, the Green Party on 8.6% and the BNP on 6.2%.