Nigel Farage has set the Brexit party’s sights on winning next month’s byelection in Peterborough, urging supporters to prepare for a possible general election.

Speaking at a press conference held to celebrate victory in the EU elections surrounded by most of the 29 MEPs who will go to Brussels to represent the fledgling organisation, he poured scorn on Conservative and Labour attempts to get to grips with leaving the EU.

The Brexit party was publicly launched just six weeks ago. It took the largest number of MEPs and won with the largest share of the national vote of all parties campaigning in the EU elections.

At the first gathering of the new MEPs, who include former libertarian and former communist Claire Fox and former Tory minister Ann Widdecombe, Farage claimed a new Conservative leader would find it “close to impossible” to take the UK out of Europe by the end of October.

“The Conservative party are bitterly divided and I consider it to be extremely unlikely that they will pick a leader who is able to take us out on the 31 October come what may.

“We might overnight have made their lives a bit easier but I don’t see them being able to deliver. I think the real barrier, the real obstruction to all of this is a two-party system that may well have worked in decades gone by but is no longer fit for purpose.”

Farage said the party’s next move would be to try to win the Cambridgeshire seat, a byelection prompted by the recall of the former Labour whip Fiona Onasanya.

“My suspicion is that we will not leave on October 31. If that happens it will be seen as the second great betrayal. That’s why what we are going to do is en masse, whether they want our help or not in getting ready, is en masse head for Peterborough and try our absolute damnedest to win that byelection,” he told the press conference in central London.

“We don’t have a great ground game, we have no data so we are starting off from a weak position. I am not going to predict victory, but I tell you what, we will run it damn close,” he said.

Voters will go to the polls on 6 June to replace Onasanya, who lost her seat after being jailed for perverting the course of justice. The seat has usually swung with the national trend between Labour and the Conservatives and 60% of the electorate voted to leave in the EU referendum.

The Brexit party would also start preparing for a possible general election, Farage said. He claimed his party would “stun everybody” if they stood across the country.

“What we are going to do over the next few weeks is to interview, to vet, to assess our 650 candidates to fight the next general election. I am optimistic that I can find men and women of this calibre,” he said pointing to the successful MEP candidates.

The party has been criticised for failing to have proper democratic structures, inviting adherents to become registered supporters instead of members.

Farage has refused to reveal the names of his donors, but the Brexit party did receive £200,000 from Jeremy Hosking, formerly a major donor to the Conservatives. The Electoral Commission announced last week it was looking into the Brexit party’s donations after the former prime minister Gordon Brown urged it to investigate concerns over the legality of its funding.

Announcing a consultation process with his party’s supporters, Farage said that reform of organisations such as the Commission would be one of the policies his party might adopt.

“What we want to do is consult directly with [registered supporters]. Like any political party, we won’t all agree with every single thing. But the main agenda will be wholesale political reform in this country – the House of Lords, the voting system, the appointments to various quangos like the Electoral Commission,” he said.

• This article was corrected on 3 June 2019. An earlier version said the Brexit party was formed six weeks ago. It was formed at the start of the year but launched publicly six weeks ago.