Zac Goldsmith's Liberal Democrat rival for the seat of Richmond Park has criticised his campaign as "ludicrous" and "nonsense", claiming the by-election is about Brexit, not Heathrow.
Mr Goldsmith resigned in protest at the Government's decision to back expansion of Heathrow, after promising to trigger a by-election if the controversial airport expansion was given the go-ahead.
The former Conservative MP for the constituency is now standing as an independent candidate.
Lib Dem candidate Sarah Olney told the Press Association: "Zac Goldsmith's idea that this was going to be a referendum about Heathrow has turned out to be nonsense because there is no pro-Heathrow candidate standing.
"Actually, what people really want to talk about is Brexit."
Mrs Olney called his decision to resign "ludicrous".
"He doesn't need a further mandate to oppose Heathrow," she said. "He already had that twice over."
Mr Goldsmith won the south-west London constituency in 2010, and again in 2015 with a 23,000 majority, but Mrs Olney is hoping pro-Europe constituents will vote for her instead.
Richmond Park voted strongly in favour of remaining in the European Union, whilst Mr Goldsmith campaigned to leave.
Mrs Olney said in the event of her election she would vote against triggering Article 50 in an attempt to remain part of the EU.
If Parliament were to trigger Article 50, the accountant said the Liberal Democrats would seek a referendum on the terms of Britain's exit from the EU.
It is not "a case of re-running the referendum", Mrs Olney said, because "there was no clear manifesto set out for what a Leave vote would mean".
The North Kingston resident said Mr Goldsmith's failed campaign to become mayor of London, in which he lost to Sadiq Khan, is affecting his support in the area.
"I have been speaking to certain groups of voters who have voted for him before but have found it worrying the way he wanted to play ethnic groups against each other."
When asked the first thing she would do if elected MP, Mrs Olney said: "Hand in my notice."
Met with laughter from members of her campaign team, she clarified: "At my old work."
Mr Goldsmith told the Press Association: "This by-election is happening for one reason only - I kept my word and resigned on principle when my former party broke its word over Heathrow.
"Obviously the concept of a politician keeping his word is an alien one to the Lib Dems. That is largely why they have been virtually wiped out as a political force.
"There is a reason why the Heathrow villagers, whose homes will be destroyed if the third runway happens, are knocking on doors for me in this election.
"There is a reason why the Heathrow campaign groups are openly backing me, despite never having backed a candidate before.
"And there is a reason why Heathrow itself has singled me out as a barrier. All of them know I am the best bet for stopping the monstrosity of a third runway."