Leave-backing Tory MPs have called for Big Ben to chime on the day the UK leaves the European Union.
But the bongs will still be halted after noon on Monday to ensure the safety of workers during the renovation of Elizabeth Tower, which houses the bell.
Earlier this year, Downing Street said Britain would leave the EU "when Big Ben bongs midnight" on March 29, 2019, the deadline for the two-year Article 50 withdrawal process.
But Commons authorities could not confirm when the chimes would start up again, or whether Big Ben would bong on Brexit day.
Tory MP Jacob Rees-Mogg told the Daily Mail: "I think Big Ben ought to be kept striking as much as possible during the repairs as long as it doesn't deafen the work force. It would be symbolically uplifting for it to sound out our departure from the EU as a literally ringing endorsement of democracy."
Party colleague Peter Bone said: "Big Ben should bong when we come out of the EU, absolutely.
"We are being liberated from the European Union superstate and Britain will again be a completely self-governing country. Where will the eyes of the world be? On Parliament and Big Ben. It would be very strange if at midnight on that day it does not chime out, very bizarre. It is the heart of our nation."
And fellow Tory Andrew Bridgen added: "It would be very fitting if Big Ben was to chime us out of the EU. We need to go out with a boom as we regain a sovereign parliament once again."
A Commons spokesman said: "On Monday, following the 12 noon chimes, Big Ben's bongs will temporarily cease.
"We cannot yet give a confirmed date for when chiming will resume, however the intent is to maintain striking for important events, such as Remembrance Sunday and New Year's Eve.
"The clock mechanism will continue to function for the immediate future, and we will aim to have at least one working clock face visible throughout the works.
"When Parliament returns, the House of Commons Commission will consider the length of time that the bells will fall silent.
"Of course, any discussion will focus on undertaking the work efficiently, protecting the health and safety of those involved, and seeking to ensure resumption of normal service as soon as is practicable given those requirements."
If the bell does not bong for four years, it would be the longest period Big Ben has been silenced in its 157-year history.
The 13.7-tonne bell was last stopped for maintenance in 2007 and before that was halted for two years in 1983 for refurbishment, but has been stopped on a number of other occasions since it first sounded in 1859.
Parliamentary officials have insisted workers' hearing would be put at "serious risk" if the bell continued chiming. They also warned those using the 100-metre-high scaffolding around the tower could also be startled by the 118-decibel bongs.
And they have dismissed suggestions the chimes could be restored during the hours that work is not being carried out as the process takes about half a day to complete.
The £29 million renovation includes the installation of a lift and repairs to the clock's hands, mechanism and pendulum.
Additional reporting by PA
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