An appeal to raise £500,000 by the weekend has been launched to ensure Big Ben chimes when the UK leaves the EU at 23:00 on 31 January.
The famous bell has only rung a few times since renovations began in 2017.
The PM’s spokesman said there could be “potential difficulties” using money raised from public donations.
But the Brexit Party’s Richard Tice said it would be “pretty feeble if we can’t organise for a bell to chime at this historic moment”.
StandUp4Brexit, the organisation behind the crowdfunder, says if it does not reach the target, the money will be donated to the Help For Heroes charity.
Appealing for contributions, the group writes: “However you may have voted in the referendum, this unique moment is unlikely ever to be repeated and if you would like to see it marked by the chiming of the most iconic timepiece in the world, please donate now.”
So far, total donations raised remain in the tens of thousands of pounds – with the largest single contribution coming from the Conservative MP Mark Francois, who has given £1,000.
Business Secretary Andrea Leadsom has said she donated £10.
Why would Brexit bongs cost £500,000?
The House of Commons Commission’s estimate is made up of two separate costs – bringing back the bonging mechanism and installing a temporary floor, and the cost of delaying the conservation work, says BBC’s Reality Check.
On the former, the commission says the floor in the belfry has been removed – work that began on 2 January in order not to interfere with New Year’s Eve.