The BBC would lose funding and influence with Ukip in power, Nigel Farage has said.

The Ukip leader has stepped up his battle with the broadcaster, accusing it of bias and undermining his party’s challenge for seats at next week’s general election.

Farage was not invited to take part in the main Question Time-style programme with David Cameron, Ed Miliband and Nick Clegg on Thursday but did take part in an individual show broadcast separately in England and Wales.

Farage has pulled out of a BBC Radio 1 appearance on Friday.

Speaking to Sky News, Farage said: “Ukip are the fourth major party in British politics and that is something that has been respected by Sky, ITV, Channel 4 and Channel 5 but not by the BBC.

“If I was in a position of power, I would take away a lot of their funding, a lot of their influence. I think in the modern world the BBC having this vast budget and this huge power over broadcasting is frankly an anachronism.”

Farage formally complained to the BBC over its decision not to include him in the Question Time leaders’ special broadcast on Thursday night. David Cameron, Ed Miliband and Nick Clegg were quizzed separately, from 8pm to 9.30pm, but Farage was not on screen until 10.30pm.

It emerged on Thursday that police had rejected a complaint by Farage over disparaging comments made on the BBC show Have I Got News For You.

The Sunday Times journalist and HIGNFY panellist Camilla Long joked on the BBC1 panel show last Friday that she had been to South Thanet, where Farage is standing, more times than the Ukip leader. “By the time I arrived there he’d only been a few times,” she said.

Farage said her comments were untrue and a breach of section 106 of the Representation of the People Act 1983.

The Ukip leader on said on Friday he believed the party was still on track to win “more than a handful” of seats in next week’s poll, including his own target of South Thanet.

Farage said: “We are exactly in the poll of polls where we were last August after we won the European elections. About 4 million people, right now, say they are going to vote Ukip next week.

“I hope we can increase upon that, I hope we can get back to discussing the real issue of British politics which is the sheer impotence of any incoming government to deal with immigration.

“It matters because of the effect on wages, it matters because of the effect on the National Health Service, on primary school education and the housing crisis in this country.

“Given there are still millions of people out there undecided, I would say Ukip is still very much in the game, we are firmly there in third place, and I am pretty optimistic.”

He added: “Short term, next Thursday, I want to see more than a handful of MPs elected, I want to see Ukip with a really good percentage score showing us as the third party in British politics and the popular vote. What will be interesting for the longer term is in how many seats do we come second in, particularly in the Midlands and north of England.”

In last night’s programme, Farage issued a staunch defence of his anger over the cost of treating foreign “health tourists” for HIV - claiming the support of a British sufferer for his stance.

The Ukip leader came under fire during a televised leaders’ debate earlier in the campaign for suggesting the cost of their drugs should instead be spent on cancer drugs for deserving Britons.

And in the latest TV set piece he brandished what he said was a letter from a patient who backed his bid to save £1bn a year by prioritising NHS help on domestic patients.

“It’s interesting. I have here a letter from a 30-year-old HIV positive man in London who says, why are the waiting rooms now full to overflowing? Why does it now take me three weeks to get an appointment,” he told the Question Time audience.

“And he says to me, it is because since we opened the door in 2012 we’re now incapable of providing HIV treatment for people legally living in Britain.”

The Daily Express said the letter was an emotional plea from a “mixed-race, gay, HIV sufferer, who says he has only 14 days worth of life-saving medicine left”.

“The waiting rooms are full with immigrant patients. Not only is this massively increasing cost it is burgeoning the small specialist system to the point of failure. Something must change and I support your comments fully,” it was reported to say.