Ukip are making significant gains in the local elections, with Conservative county council seats falling to Labour and the Lib Dems suffering a drubbing.
Ukip claimed second place behind Labour in the South Shields parliamentary by-election and after the six overnight counts, the Tories had lost 74 seats and the Lib Dems were down 16. Ukip were the big winners with 42 gains, and Labour were up 26.
Mr Farage told ITV1's Daybreak: "It's been a remarkable result for us.
"We have always done well in European elections... but people haven't seen us as being relevant to local elections or in some ways general elections.
"So for us to be scoring, on average, 26% of the vote where we stand is I think very significant indeed."
Challenged over whether Ukip were no more than the beneficiaries of protest votes against the coalition Government, Mr Farage pointed out that his party has come second in five of the last six parliamentary by-elections, claiming: "This wave of protest certainly isn't short-term - it's lasting."
Describing Ukip as "numerically" the third party in British politics, he added: "I think if we get a by-election that comes up in the next few months that is not a safe Tory or Labour seat but is a marginal, we have every chance of winning it."
Initial results in Staffordshire, where counting will continue later, saw some Labour gains and the Tories losing their stranglehold on Tamworth.
Of the six Tory-held county council seats up for grabs in the borough, three fell to Labour and a fourth to an independent candidate.
Conservative Chairman Grant Shapps acknowledged that his party had been hit by the rise of Ukip.
He said: "We have lost a lot of good councillors in the counts overnight. People have sent a message, we get it, we hear what people are saying, people are concerned that we get on with the big issues facing hard-working people in this country, like fixing the economy, sorting out the welfare system, helping hard-working people to get on."
Mr Shapps told Daybreak: "Ukip have done well, I don't make any secret about that at all. We need to make sure that we are addressing the concerns of the public.
"We have seen that we have managed to get the deficit down by a third, immigration down by a third and we are working to make sure that in this country work always pays.
"There is a lot more to do, there's two years to go until the next election and in the end it will be a choice between whether you want Ed Balls and Ed Miliband, for Labour, in Downing Street or David Cameron trying to make sure that this country is always a place where hard-working people can get on."
Tamworth's Tory MP Christopher Pincher acknowledged the impact of Ukip but said the predicted rout of his party had failed to materialise.
He said: "I think one of the key things that people have to recognise is that if you vote Ukip and you're a Conservative you end up with a Labour county councillor."
Senior politicians from the three main parties attempted to explain the rise of Ukip, which could have major implications, particularly for David Cameron as he attempts to calm the fears of grassroots Tories nervous at the loss of votes to Mr Farage's party.
Deputy Labour leader Harriet Harman told BBC One's Question Time that Ukip's rise was a "wake-up call" for the establishment parties, but some of its politics were "quite threatening".
She said: "We should listen very seriously if people are feeling disaffected and disenchanted.
"It is a challenge to us. It's a wake-up call for us to actually listen to people who feel that times are hard and wonder whether any of us have actually got the answers."
But she added: "I don't take the easy assumption 'Oh well, it's great because it's going to take votes off the Conservatives'. I think some of their politics is quite threatening and we shouldn't be complacent either."
The Prime Minister is under pressure from within his party to enshrine in law before the 2015 election his commitment to hold an in/out referendum on the UK's membership of the European Union.
Mr Cameron has promised the public a vote before the end of 2017 if he wins the next election, but London mayor Boris Johnson is among those calling for him to legislate for that commitment in this Parliament.
"I'm sure that the Government and the Prime Minister are absolutely sincere in their pledge to hold a referendum -there's no doubt about that, it's going to happen," he said yesterday.
"But maybe, just to ram that message home, some legislation would be a good idea."
Lib Dem veteran Baroness Williams of Crosby told the programme Ukip would not "last that long" as a political force and they were "essentially...trading on protest".
A Lib Dem source suggested that Ukip posed a "serious problem" for Mr Cameron and would prevent a Tory majority in 2015.
The source said: "Most people who voted Ukip are ex-Tories who don't think the Conservative Party is conservative enough.
"They pose a very serious problem for David Cameron. He must either shift the Tories to the right, and so lose centre ground voters to the Liberal Democrats, or shift his party to the centre, and split the right, helping the Liberal Democrats.
"Some people who voted Ukip did so to register a protest, and some of these used to register their protest by voting Lib Dems. We understand their frustration. And we understand why they didn't vote for us this time - because we are no longer a party of protest; we are a party of government.
"We will try to win these voters back in 2015, but not by offering protest. Instead, we will argue that it's better to be able to fix things from inside government than merely complain about them from outside government."
The source added: "These results are set to prove that the Tories can't win a majority in 2015, partly because the Lib Dems remain strong in held seats, and partly because Ukip has peeled off a significant section of Tory support."
The mauling in South Shields was "clearly a bad result" but "not a surprise in the current climate" in a seat where the Lib Dems were not expected to perform.
The Tories believed Ukip's gains were variable across the country and Labour had failed to make the progress expected by an Opposition party in a set of mid-term elections.
"On the results so far Labour progress seems very limited," a spokesman said.
Shadow communities and local government secretary Hilary Benn told ITV's Daybreak: "Ukip have clearly done very well. It's a party of protest and times are really tough. People are feeling the pain and some people are coming out who haven't voted before and expressing that by voting for Ukip."
Mr Benn added: "It's a party of protest, I don't think it's a party of government."
With Labour winning two seats in Harlow, Mr Benn said they had made gains in "the kind of places, the key seats in the south where we need to be making further progress".
The Tories have also won enough seats to retain control in Hertfordshire, where counting will continue later.
A Ukip spokesman predicted the party would receive more than one million votes, a higher level of support than at the last general election.
The spokesman said: "Where we are standing, we are taking an average of 26.2% of the vote.
"I can now predict with confidence that we will take more than 1 million votes - more than we took at the entire general election in 2010. It's likely that we might even reach 1.5 million."