Just outside the gift shop in the grand Derbyshire country house of Calke Abbey, a rack of small, brightly coloured cards has been attached to the wall, with an invitation to visitors to take one and pledge to do what it says.

“Check in on a neighbour”, suggest one. Others read: “Donate food”, “Make one extra”, “Smile”. On the rear of a card reading “Start talking” is a quote from the Jo Cox Commission on Loneliness: “Starting a conversation each day in your neighbourhood can be a radical act of community service.”

Radical acts are not something for which the National Trust, which owns Calke, is always known; nor would everyone consider that the custodian of stately homes, coastlines and countryside around the UK has a particular responsibility for community service.

But an initiative at Calke, a Baroque mansion built in the early 18th century, aims to overturn those assumptions and to challenge the issue of loneliness and isolation among its visitors and others. As well as the “pledge wall”, seating has been installed around the grounds that is designed to prompt conversations, while in three “chatty cafes” people will be encouraged to set down their cream teas, look up from their guidebooks and talk to strangers.

The plan is not to physically force people to talk to each other, says Suzanne MacLeod, who as professor of museum studies at the University of Leicester was a key member of the team behind the initiative, “but we do want to create an environment where there’s a raised awareness of the fact that we’re all in this together”.

And while this scheme has been designed specifically for visitors to Calke, says John Orna-Ornstein, the Trust’s director of culture and engagement, if visitors like them, there is no reason why the conversation-starting coffee shops - part of the national Chatty Cafes initiative – couldn’t be rolled out across the Trust’s hundreds of properties to engage its 26 million visitors each year.

Calke Abbey was acquired by the National Trust in 1981. Photograph: Neil Holmes/Getty Images

“Our purpose is specifically to care for special places,” he says, “but by doing that we give people places to gather and connect, places to be inspired and be creative, places to delight in the natural world, and to be together.

“We’re not a social-work charity, that’s not what we do, but I think we absolutely have a role in connecting people, in supporting wellbeing, in giving people good healthy lives.”

The loneliness project, part of an immersive new exhibition at the property called HumanKind, emerged from a re-examination of the history of Calke and the family who lived there, says Alison Thornhill, Calke’s community and engagement manager. Isolation has always been part of the story told at the property, in part because of the condition in which it was acquired by the Trust in 1981.

Its courtyards were overgrown, its plasterwork peeling, rooms were stashed with a jumble of broken beds, old dolls houses, and case upon case of Victorian taxidermy. Unusually, the decision was taken to leave it in a carefully preserved state of disarray, and Calke now badges itself “the un-stately home”.

Visitors, too, were told about “the isolated baronet” Henry Harpur and a ragtag collection of his descendants who were cast as eccentric or mentally ill or paralysingly unhappy.

But when the looming 200th anniversary of Harpur’s death this year prompted a reexamination of the family’s story, says MacLeod, the University of Leicester researchers found much richer and more complex stories. The “isolated” seventh baronet – a throwaway description from a contemporary who appears to have disliked him – may have been shy, but he was also “a really full individual who lived a very interesting life”, she says, marrying for love, collecting radical political caricatures and being unafraid to be unconventional.

Visitors to the HumanKind exhibition will be invited to walk through a series of the house’s more humble rooms, to which the family progressively shrunk as the estate declined in the 20th century.

The decision was taken to leave the house in a carefully preserved state of disarray, and Calke now badges itself ‘the un-stately home’. Photograph: Gary Calton/The Observer

There they can explore moving stories about other former inhabitants – among them Harriet Phillips, a housekeeper who secretly paid others to raise her illegitimate son, unable to live with him until she reached her 80s; and Airmyne Jenney, sister of the last baronet to live in the house, who was kicked in the head by a horse during the second world war and lost the power of speech.

Powerful notes from Jenney’s pocketbook made while she painstakingly re-taught herself how to talk are reproduced in one of the exhibition’s corridors, while Doris Day’s Que Sera Sera – a song she loved to blast around the house’s ancient corridors – fills the air once more. She died in 1999.

While they certainly experienced tragedies and at times were lonely, as we all are, says MacLeod, they were also able to find their way out of unhappiness to experience joy. “And every single time, the route out of it was a connection with somebody else.”

• HumanKind opens at Calke Abbey, Derbyshire on Saturday 2 March