The trio introduced themselves and their ambient music via two almost anonymous tracks posted online late last year.
Their first proper release, an EP called Metal & Dust, appeared in February, not long after they'd played their first gig in front of assembled members of the music industry.
Summer came and with it a guest appearance on Disclosure's album Settle, which promptly went to Number 1, making stars of the house duo - young brothers Guy and Howard Lawrence - and giving a platform to each of the album's cameos, including London Grammar.
It was a good break, as now the future's looking bright for singer Hannah Reid and her male bandmates Dan Rothman and Dot Major.
"It's amazing what they've achieved," says Reid of the collaboration with Disclosure. "We worked really quickly. We did that song, Help Me Lose My Mind, in two days.
"It's been great for us, being on a No 1 album just before our own album comes out. We're very grateful, and I love the song, too."
It's a far cry from the band's beginnings at Nottingham University, where Reid and Rothman were studying.
Rothman saw a photograph on Facebook of Reid with an acoustic guitar and immediately sent her a message to ask if she wanted to start a band.
Multi-instrumentalist Major, a friend of Rothman's girlfriend, was added to the line-up later, and the trio began writing songs and playing small gigs in pubs.
"I'd always written songs but I'd never performed on my own," says Reid.
"London Grammar is the first professional, or even semi-professional band, I've been in, although the boys have been in bands before."
She'd always performed in school concerts, but never had the confidence to venture out into London to play.
"It took meeting Daniel for me to be able to do it, he really pushed for me to sing live with him. I get very nervous, but I've been trying to overcome that."
The nerves could be down to her first experience of performing in London earlier this year, shortly after London Grammar put a video of Hey Now, the opening track of their forthcoming debut album If You Wait, online. It's since been viewed on YouTube almost 900,000 times.
"Because of that the gig was full of industry people," says Reid.
"Radio 1 were there, people from different labels, journalists and so on, and I knew we were being watched by the sorts of people who could really affect our career.
"We rehearsed a lot, and it went really, really well, but it was so nerve-racking."
Reid says despite the band's meteoric rise - a Glastonbury performance, top 40 single and an album that's expected to go top 10 - they don't take much notice of what's happening around them.
"We're just this band in a little nucleus. We have no perspective on how our career is going.
"We might do a show and expect 200 people to be there, but there's actually 2000 waiting for us," she explains.
The songs on If You Wait were all written by the trio. Rothman and Major tend to take care of the music, while Reid says she writes the top line to each song: the lyrics and the melody.
DAN and Dot write their music like a score and eventually after listening to it, a song will come out of it."
Before the band's UK tour in October, they're off to the States for a series of gigs.
Eventually Reid wants to play more piano on stage, and promises their sound will expand. "For now," she says, "it's about getting comfortable on stage. That's really important for me."
l London Grammar play Oran Mor on October 27. Their debut album, If You Wait, is released on Monday, September 9.