The campaigns were launched after Boris Johnson suggested that members of the public could meet the £500,000 cost of the famous bell ringing at 11pm on 31 January, when the UK leaves the EU.
Almost 30 pages on the GoFundMe crowdfunding website are trying to raise the money, but the vast majority have not received a single donation.
The few that have received support have so far raised £551 – a tiny fraction of the amount needed.
Despite the muted response, Tory MP Mark Francois, who has led the campaign for Big Ben to ring on 31 January, predicted that the fundraising target would be met within two days.
The Brexiteer, who has pledged £1,000 of his own money, told ITV’s Good Morning Britain: “I think we will get it within 48 hours.”
He added: “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 also claimed, without providing any supporting evidence, that the £500,000 cost of reinstating the bell, which has been removed for restoration, had been “massively exaggerated” by parliamentary authorities because “officials in the House of Commons just don’t want to do it”.