There are crumbs on the floor of the Art Deco living room at the Museum of the Home. The remains of an English breakfast fester on the table alongside a crumpled napkin and a white shirt is draped over the back of a chair. It all detracts a little from the streamlined glamour of the curved window, the shimmer of the cocktail shakers and the circular geometry of the tables, lamps and rugs.

The idea, museum director Sonia Solicari tells me, is to give the impression of a live interior, a glimpse into life as it was lived. This would have been a serviced bachelor flat in 1937; a maid would have cleaned up the crumbs and laundered the shirt. Glamour and grime, a life of leisure and a life of service in parallel.

But you can tell Solicari is a little uneasy. And so are the architects, Clare Wright and Naila Yousuf, as we peer into the room from behind a discreet barrier. Does it just look like they haven’t cleaned up?

In that little vignette we encounter all the promise and the problems facing the Museum of the Home, an institution that has been reimagined, rebuilt, expanded and extended while, unusually, keeping it very much as it was. This used to be the Geffrye Museum, set in an exquisite, early 18th-century set of almshouses tucked in between the council estates, gentrified terraces and former industrial buildings of Shoreditch, once the centre of London’s furniture-making trade.

The buildings were saved from demolition by the London County Council in 1911 (they would have made way for Peabody flats), partly to save one of the area’s few green, public spaces. It is an intriguing encapsulation of the issues of housing, culture, space and ownership, preservation and the poor in London. It was turned into a museum of furniture and then morphed into a museum of the home.

Home, however, is a slippery thing. It does not consist of the built fabric but the lives that people make for themselves inside it. Furniture is objects, the kind of thing you see at museums; home is an accumulation and a sense of security and belonging, a landscape of meaningful things, memories and associations.

There has been a huge shift in recent years, even in the grandest of country house museums, to counter the stories of the elite with those of the people who served them, a tumble from upstairs to downstairs. The pivot has been from the special to the everyday and the stories of ordinary people.

The Geffrye Museum was already there, with its room sets illustrating ordinary (although never actually poor) lives through the ages. “The question”, Solicari says, “is defining what the ‘everyday’ is.”

This corner of east London could hardly be a better place to ask the question. These almshouses were once situated among some of London’s worst slums. The Old Nichol, an appalling morass of darkness and crime, was around the corner and on top of it was built Arnold Circus, by the same LCC that saved the almshouses for a museum. It was the world’s first — and some of its best — municipal housing.

The neighbourhood was bombed, rebuilt, its residents rehoused, replaced, decanted and often betrayed and ignored. Now it is one of the most ethnically diverse in the country, recent immigrants living alongside gentrifying creatives. How might you represent a contemporary home under these conditions? What is the ordinary?

The room sets, scholarly scenarios of middle-class life, span the mid-17th to the late 20th century. The first has panelled walls, solid oak furniture and tapestries while the last, a loft inhabited by an imagined couple, with laminate floors and silly furniture, now looks as dated as the Restoration room.

The best of them is a 1970s interior. It’s a vivid cocktail of the cool and the commercial, not the usual restrained, mid-century, tasteful, Scandi landscape but a schmaltzy mash-up of disparate pieces and personal style, an interior that feels real and lived-in.

There’s a late Deco cocktail cabinet and a ceramic pineapple ice-bucket, a garish floral carpet and stripy golden wallpaper. There’s a spindly-legged coffee table that might have been supercool were it not for the big printed flowers, a gilded drinks trolley, a 1960s teak dining set, a plastic-fronted fake-wood sideboard and a frilly tassled standard lamp. Pictures of Jesus mingle with family photos and decorative plates. A joyful mess.

It is not quite the standard room set; rather it is the work of artist and playwright Michael McMillan, based on an installation titled “West Indian Front Room” that he curated at the museum in 2005. It’s a celebration of a hybrid culture created by immigrants who, like the artist’s own parents, made their front rooms a representational space, a faintly formal room tinged with influences from the Caribbean, from TV and from a transplanted British ideal which was then reimported to the mother country. The multiple layers of taste, class and aspiration make it extraordinarily rich, a rich sentimental stew of sauce, spice and stodge.

The inclusion of a West Indian living room goes a little way to address the provenance of the building, the almshouses built by Robert Geffrye. Geffrye (1613-1703) made his fortune at least in part from the slave trade, and was co-owner of a slave ship. His statue still stands in a niche of the building and, after a public consultation, the museum published a report and statement on its desire to “keep and explain the statue of Robert Geffrye in its current position”.

What was then still called the Geffrye became a museum of the English home during the 20th century. Yet, particularly around this part of east London, with its waves of immigration, “the English home” was never an entirely straightforward proposition.

The new parts of the building are geared towards a more nuanced representation of interior lives than the old room sets. Architects Wright & Wright’s £18.1m redesign has almost doubled the exhibition space yet feels extremely light touch. There are no flashy interventions, no grandstanding. Instead they have excavated the basements and freed up the attics, conjuring usable space where there was previously only dingy storage or artificial ceilings.

The 1990s expansion by Branson Coates, a brick horseshoe design that curves around like a pool noodle to accommodate most of the room sets, remains, and has even been re-upped by making its top-lit centrepiece the main entrance. A pub on the corner that was to be demolished in a previous, abandoned design by David Chipperfield Architects (it faced loud local opposition) now survives as the museum café and events space.

The new spaces, Solicari tells me, are not conventional galleries. Situated in former servant and storage spaces, they are tight, irregular, pockmarked with windows, doorways and abandoned openings. But that also makes them intimate and more domestically scaled, perhaps an advantage here. The stories these galleries tell are different from the more conventional interiors elsewhere.

Solicari points out the “Documenting Homes” project, which has been running since 2007 and which the museum describes as an archive that “records people’s everyday experiences of home”. It embraces a virtual scrapbook of photos, documents and objects along with their stories and testimonies, many extremely moving, small artefacts speaking of global journeys and underlining the complexity of taste, acquisition, consumption, survival and sentiment.

Photography proves an efficient way of portraying these complexities and recording disappearing aesthetics in a subtler and more individual way than merely collecting and curating a range of furniture and objects. As Solicari says, “Home is a feeling.”

The new galleries also allow for a more nuanced look at women and the home, at religious practices and even at death and loss through some wincingly sentimental but oddly captivating Victorian paintings.

A new library upstairs, due to open in September, is invitingly fitted out beneath the steep-pitched roof and its timbers. The museum’s education spaces have been expanded with rooms opening directly on to the large, elaborate and lively gardens, which constitute one of the few open, green public spaces in the neighbourhood.

Wandering through the museum, there are traces of the past picked out in subtle new details. Slim bronze strips inlaid into the concrete floors suggest the former locations of walls, nooks and fireplaces are left intact and even the shape of an old copper boiler used for laundry is retained as an enigmatic sculptural presence, a kind of inverse niche.

After more than a year of mostly staying at home, we have become increasingly, often depressingly intimate with our surroundings, the spaces and things that frame our lives. One project here, “Stay Home”, has allowed people to send in their images of working, playing, learning and doing just about everything else from home. It is becoming an incredible record of a very particular moment.

There is nothing else quite like the Museum of the Home. Perhaps, suggests Solicari, the Tenement Museum in New York, which is wonderful but which focuses on a very specific slice of immigrant life. Other museums tend to dwell on the finest artefacts, the most famous chairs, lamps or most beautiful manufactured pieces. This is not that.

This is about how even the humblest of homes reveals rich, unique stories, a recognition that culture is not only the domain of museums but of all of our front rooms, bedside tables and the snaps in photo albums (or on phones) of years of family dinners in the room with slightly ropey wallpaper, the stopped clock, those old plates and granny’s dining table.

Edwin Heathcote is the FT’s architecture and design critic

Open from June 12; museumofthehome.org.uk

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