He said Ukip was “its own force” and rejected any electoral pact with the Conservatives for next May’s general election.
Yesterday, Farage appeared with two former Tory MPs – Mark Reckless, who is standing for Ukip in Rochester and Strood, and Douglas Carswell, who last week became Ukip’s first elected MP in the Clacton by-election.
Meanwhile, the Tories and Labour remain under pressure to respond to the Clacton result, which saw Ukip winning by 12,404 votes.
Prime Minister David Cameron has come under increasing pressure from his backbenchers to consider some form of pact with Ukip next May.
But Farage insisted: “This party is not a splinter of the Conservative party. This party is its own organic force.
“We want to win our own representation in Westminster and we believe only by doing that can we fundamentally change British politics.
“To sell out so that one or two people can have ministerial positions is not what Ukip’s about.
“I don’t trust David Cameron. I don’t believe a word David Cameron says and for that reason it would be fruitless to even enter into any negotiation.”
The Conservatives have repeatedly told voters backing Ukip splits the vote and would lead to a Labour victory.
Ukip has accused the Westminster parties of running a smear campaign against them.
Addressing supporters in Rochester, Kent, Farage said the party was “targeting everybody” in the campaign to return former MP Mark Reckless, who quit the Tories to force a by-election.
A date for the vote has yet to be set by the Conservatives, who are said to be considering a long campaign, in the hope they can mobilise members to secure victory.
But a defiant Farage said: “Let’s make the people’s army of Ukip march on Rochester and Strood.”
Reckless said Ukip would “bring decisions back from Westminster” and “put local communities in charge”.
Carswell urged voters to “choose change”. He praised Reckless for seeking an electoral mandate after joining Ukip and criticised other parties for conducting “a highly personal, aggressive smear campaign” against him.
Reckless has reiterated that Ukip wants to “rebalance” immigration, which he said had held down wages and increased competition for jobs.
The Labour candidate, Naushabah Khan, said voters had more pressing issues, such as “a hospital which is failing” and “60 per cent of our primary schools which are failing”.
The Liberal Democrat candidate, Geoff Juby, said his party “seem to be out on the streets a bit more” than the others.
Clive Gregory, standing for the Green Party, said a vote for him would be “a good protest vote” whereas Ukip represented “the same nonsense as the Conservatives”.
The Conservatives have yet to select a candidate.