An "empty chair" moment then followed Mr Neil's challenge to the Prime Minister on Thursday night.
Mr Neil said the BBC has "always proceeded in good faith that the leaders would participate" in an interview, adding: "In every election, they have - all of them, until this one."
The Conservative leader is yet to agree to being grilled by Mr Neil , but he has denied claims that he is avoiding scrutiny ahead of the December 12 general election.
Mr Neil, who has so far interviewed all leaders of the main parties, said: "There is of course still one to be done, Boris Johnson.
"We have been asking him for weeks now to give us a date, a time, a venue. As of now, none has been forthcoming."
He also tore through a list of questions he wanted to ask the Prime Minister.
He added: "It is not too late. We have an interview prepared. Oven-ready, as Mr Johnson likes to say.
"The theme running through our questions is trust - and why at so many times in his career, in politics and journalism, critics and sometimes even those close to him have deemed him to be untrustworthy. It is, of course, relevant to what he is promising us all now."
Mr Johnson was interviewed by the BBC's Andrew Marr on Sunday, and was asked on why he had not agreed to sit down with Mr Neil ahead of the election.
He denied avoiding scrutiny, saying he had taken part in debates, interviews and phone-ins.
Issuing the challenge to Mr Johnson on Thursday, Mr Neil said that no broadcaster "can compel a politician to be interviewed".
But he added: "Leaders' interviews have been a key part of the BBC's prime-time election coverage for decades.
"We do them, on your behalf, to scrutinise and hold to account those who would govern us. That is democracy."