It was billed by eurosceptics as the symbolic moment that would signify the post-Brexit era: church bells ringing out on 1 February in celebration of the UK freeing itself from the shackles of the EU, a nationwide accompaniment to the bongs of Big Ben in Westminster.

But to the possible disappointment of the most fervent Brexit supporters, members of the clergy canvassed by the Guardian were not interested – and neither were the bellringers.

With church law saying that only the local parish priest has the authority to decide when bells should be rung, Leave.EU’s campaign to “let the bells ring for Brexit” immediately posed a dilemma for vicars across the country.

But after the Right Reverend Alan Wilson, bishop of Buckingham, told the Today programme that “instrumentalising church bells” to express a political view was “pretty tacky actually”, his fellow priests mostly said that they would be staying neutral.

Rev Gareth Atha, the vicar of four churches in the South Holland constituency, which had the second biggest majority vote to leave the EU, said: “We won’t be ringing the bells. We feel it’s important to remain politically neutral.”

Atha said his congregation had not asked for the local church to ring the bell. “I don’t think it would be appropriate for us to ring the bells on 1 February because of the work the church does; ministering to everyone regardless of who they are and what their political views are. It’s important we are seen to serve everyone.”

Giles Fraser, a broadcaster and parish priest in Elephant and Castle, south London, who previously described himself as a “leftie Brexiter”, warned that the campaign could worsen divisions in the country. “I am delighted we are leaving the EU, but there will be many for whom our leaving is an occasion of real pain and anger,” he said. “Leavers should not be rubbing it in through public celebrations. That is hardly the way to bring the country back together after three hard years of division.”

Church bells will not be ringing in Bolton, the constituency with the highest support for leaving the EU. A spokesperson for the Bolton parish church said the decision was out of their hands due to construction work taking place on the tower.

The campaign was also dealt a blow by the Central Council of Church Bell Ringers, which hinted that Brexit fell some way short of its standards for a moment of national unity and celebration, saying: “There are historical moments for which bells have been rung, the end of world wars, for example … [but] the council, as a principle, does not endorse bell-ringing for political reasons.”

Rev Tim Greenslade, the senior vicar at the Melbury team ministry, in west Dorset, agreed with Atha’s position that the church should remain politically neutral on the issue. That approach could be apt for his parish in west Dorset, where the result of the referendum was close, with just 51% voting to leave the EU.

Greenslade said that the day was “not a cause for rejoicing. It’s not a happy day for me … I won’t advertise the possibility of the bell being rung. If someone approached me, I’d say it’s best we keep quiet that evening.”

Rev Andy Bawtree, vicar of St Peter and St Paul in River, Kent, was the only vicar to suggest the bells could ring if there was a service beforehand. But he admitted that that was unlikely to happen. “We ring bells to call people to worship, or on other occasions, like last year in solidarity with Notre Dame, or the Olympics back in 2012,” he said. “So in the absence of a Brexit service, there will be no additional bell-ringing.”

Bawtree added that while the day marked an important change in the UK’s relationship with Europe, “the Church of England left in 1534”.