Ani DiFranco is certainly unique. A singer-songwriter whose lyrics are more startling than her melodies, she is also an impressive acoustic guitarist, influenced by American folk, jazz and punk. She is married to a man, but has a cult following in the gay scene, has staunchly radical and feminist views, and started her own record label, Righteous Babe, when she was just 20.

But there is nothing solemn about her. Now in her 40s, DiFranco bounded on stage, and performed with humour and furious energy, treating the audience as if they were close friends sharing her intimate songs and chat about her relationships with her husband and her mother. Dressed in defiantly anti-showbiz style – plain top and brown trousers – she announced: “I’ll be doing different songs tomorrow, so if I’ve sung your favourites, stay at home.”

For this show, she started in the mid-90s, with the on-the-road song Dilate, followed by the driving Angry Anymore. A half-spoken folk-rap story from her busking days on how “those who have the least give the most” included her rapid-fire guitar work, backed by a rhythm section of Todd Sickafoose on bass and celebrated New Orleans drummer Terence Higgins. Her last album included angry political songs, but Allergic to Water, released in November, is different. “There are lot of ‘married with kids’ songs,” she explained, adding: “I tried to raise my daughter gay, but it’s not working.” The new material included the cool, drifting Careless Words, “on how marriage is hard sometimes”, and a more conventional and cheerful love song, See See See See.

Then it was back to the angry 90s for a finale that included Untouchable Face, an outpouring of jealousy with the chorus “fuck you for existing in the first place”. DiFranco is an exhilarating performer.

• At Union Chapel, London, on 23 September. Box office: 020-7226 1686.