Britain needs to take special measures if it is ever to recover from the scarring social divisions exacerbated by Brexit, says a working party drawn from the country’s leading institutions.

The Guardian understands one of the initiatives that has caught the imagination of the group is the creation of the post of “healing tsar” – a unifying figure to promote a feeling of national togetherness. Several well-known figures have been sounded out for the role, although there are worries that the politicians involved will try to parachute their own preferred candidate into the job.

Operating in secret, the group is studying a series of proposals to “put harmony back into the national mood, to sow accord where there is discord, collaboration where there is conflict”. Music is seen as vital to the task.

The idea was first mentioned privately by Prince Charles, who, although he has kept his views on the EU to himself, is said by insiders to be deeply troubled by what he sees as a dislocation between the people and the institutions of the country.

Senior sources close to official figures say he fears the royal family could be drawn into the bitter divide – one of the reasons why he and his wife, Camilla, Duchess of Cornwall, absented themselves on a trip to Cuba during the 1 million-strong march through London and the parliamentary climax of the Brexit process.

In heated meetings behind closed doors at Thenford House in Northamptonshire, the estate belonging to Michael Heseltine, the Liberal Democrat representative argued strongly for party supporter Bob Geldof as “healing tsar”. One insider promoting Geldof’s credentials said: “He brought the country together with Live Aid – he can do it again.”

Facebook Twitter Pinterest Is Bob Geldof the right person to bring the country together again? Photograph: Mark Metcalfe/Getty Images

Those close to Geldof say he is reworking his biggest hit, Do They Know It’s Christmas? – but with the chorus changed to: “Heal the island, let them know it’s bonding time.”

A sticking point is said to be the insistence of the Lib Dem leader, Vince Cable, that he perform the reworked classic with Geldof. The former Boomtown Rat has been quoted by a source as saying: “I’m not going on stage with that old fooker.”

Labour, though, is not keen on Geldof, whom they regard as a loose cannon. They are pushing the case for Alice Nutter, the former singer with the anarcho-punk group Chumbawamba.

The band’s big hit, Tubthumping – “an anthem of defiance for the ordinary and oppressed” – is, Labour believes, ripe for revival and perfectly encapsulates these divisive times with the key lyrics: “I get knocked down, but I get up again / You are never gonna keep me down.”

Facebook Twitter Pinterest Labour believes Alice Nutter can help Britain get up again. Photograph: Christopher Thomond/The Guardian

Nutter described herself in a recent interview with the Guardian as a “sort of Communist-Marxist” but said she goes out knocking on doors, selling the Jeremy Corbyn message. Labour insiders believe Nutter’s added advantage would be to emphasise the cutting of the umbilical link with New Labour by reviving memories of Chumbawamba’s most famous moment: pouring water over John Prescott’s head at the Brit awards.

The Conservative representative has told colleagues the party favours a more low-key approach. It is understood they have nominated David Van Day, who gained national fame in the 1970s with the popular duo Dollar – moving on to Bucks Fizz in 1990.

Van Day, who once during a fallow patch in showbiz managed a burger van, was recently elected as a Tory councillor in Thurrock. Supporters say a re-recording of his 1998 hit, There’s a Whole Lot of Loving, could become the anthem of the healing process.

The group is also considering a number of events to help with reunification of the country. One idea gaining traction is for a 12-hour live TV recreation of the popular show It’s a Knockout, which ran for 15 years on the BBC. It would feature combined teams of commentators and MPs based on remainers v leavers. “We’re looking at a more no-holds barred contest – let’s let off steam, let’s get this done,” said one source with knowledge of the talks.

Facebook Twitter Pinterest David Van Day – seen here as part of pop duo Dollar – is the Tory choice for ‘healing tsar’. Photograph: PA

Among locations suggested for the contest are Edgehill in Warwickshire – the site in 1642 of the first pitched battle of the English civil war – in which the casualties numbered more than 4,000 killed and wounded.

Also at an advanced stage in the discussions is the idea of a “Festival of Britain” – although the Democratic Unionist party has initially said no, arguing it must be called the “Festival of Great Britain and Northern Ireland”. The festival – an echo of the 1951 national exhibition and fair – would celebrate the achievements of the country and foreign participation would be banned.

Again the site could prove an issue. The DUP is demanding that its support is conditional on firstly, “money-on-the-table”, and secondly, it must be held in the Fermanagh and South Tyrone constituency of the party leader, Arlene Foster.

If they can settle on their preferred person as “healing tsar” after a series of behind-the-scenes indicative votes, it is expected the tsar will make their debut at the Healing Field during the Glastonbury festival in late June, where festivalgoers will be invited to “chill out and soak up the vibe”.