The Brexit Party, which was established in April, swept to victory in the United Kingdom's European Parliament election last month, riding a wave of anger over Prime Minister Theresa May's failure to deliver Brexit on time.
The nominations process for the new leader will be completed on Monday, with candidates requiring the support of eight MPs to enter the race.
She had said in an emotional press conference that she was sad because she has not been able to pass her Brexit deal through the parliament in three attempts.
Her team has been keen to shape her legacy beyond the Brexit failure, but she bequeaths to her successor a nation where traditional political divides are being eroded by strong beliefs on whether Britain should leave the European Union, and how it should do so.
Labour, which along with the Conservatives saw its support slump at the European elections as voters expressed their frustration over the Brexit deadlock, is divided over whether to unequivocally support holding a second referendum.
The Conservatives and Labour will be clinically analysing the Peterborough result to gauge the likely impact in a general election.
But she finally acknowledged defeat in a tearful resignation speech last month, the culmination of months of political turmoil that had slowly sapped her authority.
The result is a setback for the Brexit Party, whose candidate Mike Greene (C) failed to make the breakthrough the party had been hoping for.
But Mr Trump used the trip to speak with Mr Johnson and other candidates to replace her, emphasising where the political power in Britain now lies.
Former foreign minister Boris Johnson is seen by the bookmakers - and many party activists - as the favorite in the race, which now features 11 candidates. Further rounds will be held on June 18, 19 and 20 if needed, with the least popular candidate eliminated each time.
Other front runners are playing catch up, with the current foreign minister, Jeremy Hunt, and environment minister Michael Gove taking a more moderate stance on Brexit.
"I believe that European leaders want to find a way through this", Gove wrote in the Daily Mail.
But the chances Britain's 27 European Union partners would consider reopening the legally binding divorce agreement appear slim at best.
Hard-core Brexiteers in the British leadership contest say they would rather take Britain out of the bloc with no deal than countenance a further delay. The prospect poses a dilemma as numerous party's supporters backed Brexit.
Brexit is still scheduled for 31 October but while her rivals thrash it out, the project remains stuck, with the only divorce plan agreed with Brussels stuck in parliament.
Mr Farage's endeavour to "challenge the insular political class" and "push for fundamental democratic reform across our unrepresentative political system" through devolving aspects of decision-making to its members evokes one of the mechanisms of the Italian anti-establishment Five Star Movement, which employs direct democracy on policy including proposing laws and even holding confidence votes in its party leader.
The Peterborough election was triggered when Labour's Fiona Onasanya became the first member of parliament to be ousted in a recall petition, after she was jailed for lying about a speeding offence. "I look back and I think I wish I hadn't done that", he said.