One of those calling for a rethink to stop Big Ben being silenced for the longest period in its 157-year history, Labour MP Stephen Pound, said he hoped at least 20 "like-minded traditionalists" would gather to witness the halting of the bongs.
Earlier this year, a spokesperson for the prime minister's office at 10 Downing Street said Brexit would come into effect "when Big Ben bongs midnight" in the first second of March 30, 2019. A round of polite applause rippled through the crowd once the last bong had faded away.
Renovation works will take place on Parliament's bell, clock and tower.
Tom Brake MP, spokesman for the Commons commission responsible for maintaining the Houses of Parliament, said the works were probably the most substantial ever carried out on the tower.
It will be disconnected and will sound more the hours as it had done since 158 years nearly without interruption, accompanied by a carillon of four bells smaller for the quarters of an hour.
May's comments were more restrained than those of her Brexit minister, David Davis, who said on Tuesday that the silencing of Big Ben for such a long period was "mad".
Some have argued that silencing the iconic bell during renovation work is unnecessary.
It means silence for Big Ben - which is the name of the bell inside the clock, though it's commonly used for the landmark itself. The original mechanical clock mechanism is to be completely dismantled, refurbished and put back together in a separate operation taking around two years.
Lee, who owns Thwaites & Reed, one of the UK's oldest clockmakers, which maintained the Great Clock at Westminster for more than 30 years from the mid 1970s, said: "There is something amiss. Constant proximity to the chimes would pose a serious risk to their hearing, and would prevent efficient working".
However, it will still sound on big occasions such as New Year's Day and Remembrance Sunday.
And now the clock's cogs and hands, as well as the four dials, will be removed, cleaned up and repaired as part of the work.
He said: 'Why shouldn't there be a round the clock effort to get it done?
Big Ben's last bong!
In response to the criticism, House of Commons officials have said they will take another look at the repairs schedule once Parliament returns next month from its summer break.
A brick enclosure in the tower will be replaced with glass to allow Big Ben to be viewed by people walking up the staircase.