Margo Price isn’t playing guitar tonight – waving, in its stead, a tambourine adorned with a scarf. “I shut my finger in the car door,” she explains.

Untethered from her instrument, the emerging country star prowls around the stage, grinning, waving, winking and cracking dirty jokes. The next song is Since You Put Me Down, a terrific lament about “drinking just to drown” – the sort of good-time tune about bad times that has long characterised the country genre. It starts gently, with just Price’s clear, cool voice and her partner, Jeremy Ivey, taking her place tonight on acoustic guitar. Then the full band kick in – plangent lap steel, succinct electric guitar, and a twinkly rhythm section, shimmying far more than you expect.

“I’m an outcast and I’m a stray/ And I plan to stay that way,” Price sings, as the song hits the last of its series of emotional peaks. It is hard to imagine this charismatic artist spending a decade in her previous band (Buffalo Clover, they were called) playing to “nine people and a cardboard cut-out of Kenny Chesney” (as she told one interviewer); of routinely being ignored in Nashville. But apparently, it was so. She introduces another great song, about a particularly terrible tour of Florida. Desperate and Depressed, it’s called.

Price’s painful hand is, then, just the latest in a long line of calamities and contretemps that have, with no little irony, made her one of the most appealing new voices coming out of the US this year. Most of her hardships are laid bare on her debut solo album, Midwest Farmer’s Daughter – clustering particularly on its opening track, Hands of Time.

She plays it tonight with restrained emotion. Things went south when Price’s daddy lost the farm – literally. She tried to make her own way, “bustin’ my ass”. She romanced a married man. They worked the land. Her first-born died. She turned to drink. She crashed the car and spent the weekend in the county jail (the subject of another great song, Weekender).

Bewilderment and doggedness trade off in Price’s autobiographical ballad. “I wanna buy back the farm,” swells the chorus, “and bring my momma home some wine/ And turn back the clock on the cruuuuuuel hands of taaaahme.” Only a slab of granite could remain unmoved. Price couldn’t be more “country” if she had a piece of hay covered in rhinestones sticking out of her mouth.

Midwest Farmer’s Daughter came out in March to much acclaim, mostly from outside the country music world. The record was released on Third Man, the label run by Jack White and his associates, rather than a more traditional stable. Midwest Farmer’s Daughter went top 10 in the Billboard country chart on release, but without a song gracing the country singles chart – governed by country radio airplay, from which Price was largely excluded.

Price actually pawned her wedding ring in order to record at Sun Studios. And yet she operates from outside the tent – a fact reinforced recently, when the Country Music Association announced its nominees for this year’s gongs. Despite her high charting, Price was snubbed, alongside another outlier, Sturgill Simpson, whose own song cycle concept album didn’t jump through the right hoops for the establishment, either.

“I wrote this song as a kind of middle finger to Nashville,” Price says, introducing This Town Gets Around, “and they gave it right back to me.” It’s another romp, this time around the double standards and mercenary nature of country’s home town. “It’s not who you know, but who you blow that’ll put you in the show,” Price trills.

Tonight’s show would have been special had it merely been a playback of Price’s excellent album, studded with a few well-chosen covers (Loretta Lynn’s Rated X, George Jones’s Heartaches and Hangovers, but Bob Dylan and Neil Young too).

An extra frisson comes from the surprise arrival in London of Price’s producer, Alex Munoz, who has been in Spain receiving cancer treatment. “He’s cancer-free,” announces Price, choking up a little; Munoz joins them on mandolin on a barnstorming version of Tennessee Song.

At one point, the lights fail. A twinkle of mobile phone torches and discreet house lights illuminate Price’s beaming performance, as she finally straps on her guitar, pain or no pain.