Farage, who stood down as Ukip leader before being reinstated four days later, says his party’s greatest potential is in Labour areas

Nigel Farage has suggested he would like to fight a Labour-held seat in a byelection, suggesting he has not given up on entering parliament after his seventh bid to be an MP failed last week.

The Ukip leader, who stood down when he was defeated in South Thanet only to be reinstated four days later, does not appear to be getting the break from politics that he said he wanted.

In a number of broadcast interviews over the past two days, Farage has set out his desire for Ukip to play a major role in the debate about the EU referendum, which may be brought forward to 2016.

Asked about his future ambitions on BBC Radio 5 Live, he said: “I would look forward to a byelection in a Labour seat very much indeed.”

Farage said his plan was to argue for electoral reform and an EU referendum on terms that were fair to the “out” campaign.

He strongly denied that his return suggested he runs a one-man-band, saying it was simply a sign of a party with “overwhelming support for its leader”.

Ukip denied a report on the rightwing Breitbart News website that Farage had effectively forced his colleagues to re-appoint him by staying in the meeting where Ukip executives voted on whether he should remain as leader.

Ukip chairman Steve Crowther said: “There was not the slightest suggestion that the NEC was anything other than unanimous in its wish for Nigel to withdraw his resignation. He spent a considerable time making the case for his resignation and the appointment of an interim leader, but there was no one in the committee who did not want him to stay on. He left the room while it was further discussed.

“I took the views of members and they unanimously asked him to remain as leader. The NEC is 100% behind Nigel as we go forward into the referendum campaign which is already under way.”

There are further reports of a split within Ukip about whether to accept all of the public funding, known as short money, to which they are entitled – about £650,000 – on the basis of their election results.

Ukip failed to live up to its own expectations at the election, holding only one seat and losing another. However, the party is claiming it as a victory that it got about 4m votes and came second in 120 seats, mostly in the Labour-held northern England.

Farage told BBC Radio 5 Live that he thought Ukip’s greatest potential was in Labour areas. “Ukip significantly helped the Conservatives win this election by tearing vast chunks out of the Labour vote in the north and the Midlands,” he said.

Asked about the candidates for Labour leader, he said most of the contenders appeared to be from an out-of-touch metropolitan elite. But he conceded: “I would have been very fearful if [former army officer] Dan Jarvis had stood ... he is at ease talking to ordinary folk.”

Since Ukip’s defeat, there has been speculation that the party’s single MP Douglas Carswell, could re-defect to the Conservatives. He gave a less than enthusiastic response to the news that Farage was making a comeback as leader, refusing to comment to reporters when the news emerged.

However, when asked on Twitter whether he was staying in Ukip, the MP replied: “Of course I am. Bizarre string of tweets suggesting otherwise!... sparked by a couple of loopy journos ....”