The hopes of diehard Brexiters to hear the chimes of Big Ben sound at the moment the UK leaves the EU appear to have finally been dashed by Downing Street, as it indicated this will not happen even if the public raises the £500,000 needed to pay for it.

According to Boris Johnson’s spokesman, Commons authorities – who warned on Tuesday of the high cost of completing the complex restoration of the clocktower – have said there could be difficulties in accepting public donations.

On Tuesday, the prime minister said the government was “working up a plan so people can bung a bob for a Big Ben bong”. However, it transpired that there was no such plan, and the House of Commons Commission, which organises the running of parliament, said the bell was “unlikely” to sound at 11pm on 31 January, the moment Brexit officially happens, in part due to the estimated cost of £500,000 to make it happen.

Work needed would include restoring the clock chime mechanism, testing it, building a temporary floor in the belfry to allow the work to take place and delaying other restoration work for several weeks.

After it emerged that No 10 had no mechanism to raise the money, several crowdfunding pages were set up, and one of these has so far raised nearly £70,000.

But speaking on Thursday, Johnson’s spokesman indicated the Brexiters’ dream seemed doomed even if the sum was raised.

“The House of Commons authorities have set out that there may be particular difficulties in accepting money from public donations,” he said. “The PM’s focus is on the events which he and the government are planning to mark 31 January.”

Asked if people should thus not bother giving to the crowdfunder, he replied: “I’m just reflecting that the parliamentary authorities have set out some potential problems and our focus is on the events that the government is currently working on.”

Downing Street has promised to unveil a package of events to mark Brexit, but has yet to give any details. The programme is expected to be relatively low-key, with an emphasis on avoiding perceived triumphalism on what is still a hugely divisive issue.