Located within walking distance of each other in Shoreditch, the spaces are designed to encourage local residents, workers and visitors to cross paths.
"There are nowadays many communities in Shoreditch that are overlapping each other," Khan told Dezeen.
"You've got the tech startups, you've got Friday-night traffic of people coming out to party, you've got an established residential community, and it's an incredibly busy thoroughfare for cars and pedestrians."
"Those communities don't cross positively. They don't help each other or learn from each other," he continued. "What we tried to do here is create a space that the different communities can all use."
The plant-filled spaces – named Connect, Create and Relax – are underpinned by the Japanese idea of shinrin-yoku, which translates as forest bathing.
The Relax room, located on the junction of Old Street and Pitfield Street, is elevated from the ground. Visitors have to walk up a small hill made from rubber mulch to crawl into it through its base.
The Create structure is located in Charles Square in the middle of a residential estate. It features bleacher-style seating and power outlets for visitors' phones and laptops.
The final room, Connect, is a corridor-like space installed in the square next to Shoreditch Fire Station. Inside this space is a long communal table intended to encourage passersby to meet and interact.
Each of three rooms is made from layers of corrugated plastic sheeting. At night, LEDs trapped within the plastic walls illuminate the space, giving off a soft glow.
The rooms have been filled with plants specially picked out by horticulturalist Jin Ahn. Visitors are encouraged to take away plants, and can also donate plants that they cannot look after anymore.
"It's nice to see the city changing around us, but on the other hand we feel we're losing things that we grew up with that the new generation can't access anymore," said Khan at the unveiling.
He believes we are living with fewer civic spaces, like libraries. "The idea that you take the plants away from here is from the library model," he said. "People will take the plants, and people can bring things here that they've out grown".
At 36, Asif Khan is one of a generation of emerging young British architects that are attracting international attention. He recently made the shortlist for the Guggenheim Helsinki and won the competition to design a new building for the Museum of London.
Forests is a continuation of MINI Living, a project from the car company based on predictions for future city living. MINI Living began with an installation during this year's Milan design week.
MINI Living Forests is open to the public during the London Design Festival, which takes place from 17 to 25 September 2016.
His other projects include an installation in Melbourne's Federation Square, and an elevated wooden play area at an east London primary school.