Mark Francois, who has promised £1,000 from his pocket, predicts the sum will be raised “within 48 hours”, allowing the time needed to ready the bell.
But he criticised the House of Commons officials in charge of the iconic tower for “massively exaggerating” the cost estimate.
The bell is currently silenced amid extensive renovation works on the Elizabeth Tower, but Brexiteers are determined to bring it back to life to mark Britain’s departure from the European Union.
Health Secretary Matt Hancock is the latest to give the campaign his backing, saying he would “love to hear the Big Ben bong on Brexit day”, after Boris Johnson’s “bung a bob for a Big Ben bong” pitch on Tuesday.
No official campaign has been launched, with the government ruling out leading one yesterday. It has so far drawn muted support on crowdfunding websites.
Whether Big Ben bongs or not, Nigel Farage, the Brexit Party leader, said on Wednesday that the Leave Means Leave group had gained approval to stage a celebratory event in Parliament Square on January 31.
Meanwhile, Leave campaigners’ calls for church bells to peal across the nation at 11pm on January 31 to echo the flood of chimes for the Allies’ Second World War victory in 1945, were also facing stiff opposition.
“Whichever way you look at it, February 1 will be the most momentous morning in British history since the glorious day in 1945 when our country celebrated victory over the Nazi regime in Germany,” Leave.EU said.
But the Central Council of Church Bell Ringers declined to give its backing, saying in a statement that it “does not endorse bell ringing for political reasons”.
Mr Francois told ITV’s Good Morning Britain: “It seems to me and many of my colleagues in the House of Commons patently daft that we have got the most iconic clock in the world – literally, it’s a world heritage site – that that should stay silent on this occasion.”
He claimed the costs were “massively exaggerated” because “officials in the House of Commons just don’t want to do it”.
Restoring the bell was discussed at a meeting of the House of Commons Commission on Monday, but it was ultimately ruled out after it was revealed that it could cost £500,000.
Commons Speaker Sir Lindsay Hoyle, who is chairman of the commission, said: “You are talking about £50,000 a bong.”