Jubilant Ukip leader Nigel Farage said his "people's army" was on its way to Westminster after securing first place in historic elections for the European Parliament.
Mr Farage said that the eurosceptic party will "give it our best shot" in next week's by-election in Newark - an area where it finished top last night despite trailing the Tories by 25,000 votes in the 2010 general election - and was hoping to secure "a good number" of MPs when the country goes to the polls in May 2015.
Liberal Democrat leader Nick Clegg insisted he would not resign, despite pressure for a change in leader from activists horrified by a disastrous night for the party, which lost all but one of its 12 MEPs and trailed in fifth in the national vote and sixth in Scotland.
Former MP Sandra Gidley said the Lib Dem brand had become "toxic", while Lib Dem MP John Pugh said he wanted Business Secretary Vince Cable to take over as leader, warning that a fundamental cause of the Lib Dems' "abysmal" showing was the fact that voters were no longer willing to listen to Mr Clegg.
"If we carry on as usual, we are like the generals at the Somme, because these losses are horrendous," the Southport MP told the BBC News Channel. "Given the scale of the losses, to call for business as usual is frankly ludicrous."
Speaking at Lib Dem HQ in central London, Mr Clegg said the results in local and European elections were "gutting and heartbreaking", but insisted he would not resign, vowing to "finish the job".
Following criticisms of his decision to take Ukip on directly over EU membership - including in a pair of TV debates with Mr Farage which he was widely judged to have lost - Mr Clegg said: "It didn't work but it was right that we stood up for the values we believe in.
" Of course it is right to have searching questions in the wake of such a bad set of election results but if I'm honest the easiest thing in politics - just as in life - sometimes when the going gets really tough is just to walk away, to wash your hands of it. I'm not going to do that and my party is not going to do that."
Arriving to address supporters at a victory party, Mr Farage made clear his eyes were on the Newark by-election on June 4, where Conservatives are defending a 16,152 majority.
"The people's army of Ukip are on their way to Newark," he said. "We are going to give it our best shot."
Summing up the aftermath of last night's results, he said: "Nick Clegg's in the most trouble, Ed Miliband's in quite a lot of trouble, David Cameron's in some trouble.
"If we were to win Newark, David Cameron would be in even more trouble than Nick Clegg. If we were to overturn this massive majority they have got, it would be a very hot, long summer in the Tory Party."
Asked whether his stunning victory was the result of a protest vote, Mr Farage said: "It's beginning to look like a permanent protest."
After votes were counted in all 11 of Great Britain's constituencies, Ukip was dominant with 24 MEPs, including one in Wales and its first representative in Scotland. Its 27.49% share of the national vote was up 10.99 points from the last Euro elections in 2009, when it secured 13 seats.
It was the first time for more than a century that a national vote has not been won by either the Conservatives or Labour, as voters turned away from mainstream parties throughout Europe.
David Cameron came under pressure to consider an electoral deal with Ukip amid fears that the two parties could split the right-of-centre vote in the May 2015 general election.
Mr Cameron insisted he was not ready to countenance any pact with Ukip, saying that all-out victory for the Conservatives was "achievable" and was the only way to guarantee an in/out referendum on Britain's membership of the European Union (EU).
Ed Miliband insisted that Labour was "in a position where we can win the general election", despite disappointing results which saw the party perform strongly in London but barely scrape into second place nationally, less than two percentage points ahead of the Tories.
With counting completed in England, Scotland and Wales, Labour had 20 MEPs and a 25.4% vote share, the Tories 19 MEPs and a 23.93% vote share, the Greens three MEPs and a 7.87% share while the Lib Dems managed a solitary MEP and 6.87% of the national vote.
The Scottish National Party held onto its two MEPs and led the pack with a 28.9% share of the vote north of the border, ahead of Labour on 25.9%, Tories on 17.2% and Ukip on 10.4%. Liberal Democrats came sixth in Scotland.
Votes were being counted in Northern Ireland over the course of the day.
Mr Farage described Mr Clegg's position as "untenable" and said he would be "very surprised" if he remained in post until next year's poll.
But the man often tipped as Mr Clegg's most likely successor, party president Tim Farron, was vocal in his loyalty, praising the leader for his "backbone" in standing up for the unpopular European cause while Cabinet minister Danny Alexander warned critics against plunging the party into a damaging period of introspection.
Former leader Sir Menzies Campbell insisted it was not time for "a black tie... and funereal voice", insisting: "There's no doubt in my mind that Nick Clegg is the person with the courage and the resilience to take the party through to and during, and indeed after, the next general election."
Mr Miliband insisted the local and European elections showed Labour making "progress", although there was "further to go".
He said the results showed there was a "desire for Europe to work better for Britain" but rejected Mr Farage's suggestion that Labour would now have to change its policy and guarantee an in-out referendum in the next Parliament.
"We set out our position for the general election on the European referendum. We will have a referendum if there is any transfer of powers from Britain to the European Union," he said.
Shadow business secretary Chuka Umunna acknowledged that next year's vote was not "in the bag" for Labour and said the party - which has been accused by some activists of failing to confront the Ukip threat - must now take the debate with Mr Farage's party "seriously".
Mr Cameron blamed "deep disillusionment" with the EU for Ukip's stunning poll victory - but again dismissed as a "myth" the prospect of an electoral pact with the party.
The Tory leader was coming under pressure to consider a deal with Ukip, with re-elected MEP Daniel Hannan pointing out that together the parties commanded more than 50% of the national vote.
"It would be very sad if the two right-of-centre eurosceptic parties at the general election 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," Mr Hannan told Sky News.
But Mr Cameron told Radio 4's Today programme: "Conservative candidates will stand as Conservatives, fight as Conservatives and, I hope, win as Conservatives. We are not going to be doing deals and pacts."
The premier ducked the question of what disciplinary action would be taken against Tory candidates who struck local arrangements with Ukip, saying only: "I don't see any prospect of this happening."
Mr Cameron declined to say whether he would opt to form a coalition with Lib Dems or Ukip in the case of a hung Parliament, insisting: "Between now and the next election, I'm only going to be talking about my goal, which is all-out Conservative victory, and I believe that is achievable."
Mr Farage said he would be "relaxed" about local arrangements between Ukip and eurosceptic-sitting MPs from either Labour or the Tories, but expected them to be vetoed by Conservative high command. A national deal with Tories was not in his party's interests, he added.
In a press conference in central London, Mr Farage said that what he described as the "legacy parties" were "like goldfish that have just been tipped out of the bowl onto the floor, desperately gasping for air and clinging on to the comfort blanket that this is a protest vote".
He said: "This is an earthquake in British politics, it is a remarkable result and I think it has profound consequences for the leaders of the other parties."
Mr Farage said he was "extremely grateful" to Mr Clegg for challenging him to a pair of TV debates, which he said had "allowed us for the first time in 40 years to put the argument why this country is better off outside a political union."
He said: "I find it very difficult to believe he will lead the Liberal Democrats into the general election."
The Ukip leader said he believed Mr Miliband would be forced to offer an in/out EU referendum by the time of the Labour annual conference in the autumn, and warned he would become "Ukip's greatest recruiting sergeant" if he failed to do so.
Although Mr Cameron was the "least scathed" of the party leaders last night, his test would come in Newark in 10 days time, said Mr Farage.
"Ukip, with the wind behind it, has got momentum," he said. "The plan short term for us is very simple. The people's army of Ukip now marches on Newark. We will do everything we can in the next 10 days to help and aid Roger (Helmer)'s candidacy.
"We are going to do our damnedest to try to pull off an even more spectacular result. If we do that, I suspect Mr Cameron will also begin to feel some of the pressure."
Mr Farage accepted there was no prospect of Ukip winning next year's general election, but said that it was "perfectly realistic" to think that it may be able to pick up seats where it has strongholds in district and county councils, naming Great Grimsby, Boston, Yarmouth, Thanet, Folkestone, Portsmouth, Plymouth, Aylesbury, Rotherham, Eastleigh and parts of Cambridgeshire as targets.
"Our game is to get this right and find the right candidates and target our resources on putting a good number of seats in Westminster next year," he said. "Who knows, if Ukip hold the balance of power then there will be a referendum."
A Labour councillor has branded Ukip voters as "thick and ignorant".
Fabian Breckels, a Bristol City Councillor, made the comments on Twitter in the wake of Farage's party's historic victory during the European elections.
Ukip won two of the six MEP seats in the South West of England and was close to winning a third.
Councillor Breckels, who represents St George East, tweeted: "What is really worrying about #Ukip voters is most have no idea what #Ukip really stand for. Too thick and ignorant to care. Frightening."
Conservative former deputy prime minister Lord Heseltine said Ukip's surge in support was the result of discontent over the economic downturn and would fade.
He insisted that there should be "no pact under any circumstances" with Mr Farage's party.
"If you say to me 'are they going to be a major force in the next general election?' the answer is no," Lord Heseltine told BBC2's Newsnight.
"It was the place to go to protest about certain things that have been happening which they associate with Europe, but the real problem is the recession. Whenever you get a recession of this sort, mid-term election results find a protest point. It used to be the Lib Dems."
Lord Heseltine said that immigration had been "hugely good throughout the centuries" for Britain by bringing in "wave after wave of huge talent".
He said Mr Cameron should "certainly not" bring forward his planned date for the referendum from 2017, saying: "Getting agreement at all will be hard, but to think you can stampede 27 other countries into agreeing what you want in a matter of months and get the legislation through, and all that, is simply wrong and irresponsible.
"It would be crazy to either try to rush it, which would just create alienation on the continent, or secondly to bow to what people are now demanding, which is 'Tell us exactly what you are going to demand'."
Lord Heseline said there were racists amongst Ukip members and that an electoral pact would "split the Tory Party" and make it "very difficult" for him personally to vote Conservative.
"The principle that the Tory Party is associated with the sort of undercover approach and attitudes of much of the Ukip party would be quite unacceptable to a huge swathe of moderate one nation Conservatives," he said.