Linda alone
Linda lost her voice for the next two years as a result of spasmodic dysphonia. She made a new start in 1984, singing with "Home Service" at the National Theatre's production of The Mysteries and in 1985 she released her solo album One Clear Moment, then fell silent for eleven years. One song from the album, called "Telling Me Lies", written with Betsy Cook, was recorded by Emmylou Harris, Dolly Parton, and Linda Ronstadt for their Trio album in 1987. The recording was nominated for a Grammy in the Best Country Song category. Linda retired from music to run an antique jewellery shop in Bond Street, central London. She married Steve Kenis, an American recording artists agent at William Morris.
A compilation of Linda's earlier work, Dreams Fly Away (1996), included both previously released songs and alternate versions of some of her better-known songs. It was received politely but did not sell well. In 1999, Linda's mother died. This provoked an outpouring of sorrow and regenerated her determination to sing. Linda was diagnosed with spasmodic dysphonia, preventing her from singing. A temporary cure was found. By having botox injected into her throat, she could regain her normal singing voice for a few months. Give Me a Sad Song (2001) was positively reviewed. In 2002, she released a new CD, Fashionably Late, which featured several family members, including her son Teddy Thompson and daughter Kamila Thompson, as well as an appearance on one song by Richard Thompson.
Linda appeared along with her son Teddy, her friends The McGarrigles, and Kate McGarrigle's children Martha Wainwright and Rufus Wainwright (amongst others) in Hal Wilner's "Came So Far For Beauty" tribute concerts to the music of Leonard Cohen from 2003 to 2006. Linda sang the Cohen songs "A Thousand Kisses Deep" and "Alexandra Leaving". She appeared again with Teddy Thompson with The McGarrigles and Wainwrights for some of their family concerts, including the McGarrigle Christmas shows. In 2007, Linda released yet another set of original songs and covers, Versatile Heart. Like Fashionably Late, this too was primarily a collaboration with son Teddy Thompson, and the CD also features a supporting cast of family and friends. The CD was well received in the press. The CD opens and closes with two arrangements of a Teddy Thompson instrumental piece, "Stay Bright", the first an acoustic version, and the second a version for string quartet arranged by Nick Drake collaborator Robert Kirby. She contributed vocals to the Primal Scream album Beautiful Future (2008), on the track "Over & Over".
Linda and Richard Thompson performed a duet at 12 June 2010 Meltdown Festival tribute concert to Kate McGarrigle, which Richard coordinated.
Linda's fourth solo album, Won't Be Long Now, was released on 15 October 2013. The album features compositions and backing vocals from Teddy Thompson and his sisters as well as guitar work by Richard Thompson.
Linda appears on the album Family (2014) by the band Thompson (named for all the Thompsons that appear) having written two songs for the project. The album was produced by her son Teddy Thompson and features Richard Thompson and The Rails, who are Linda's daughter Kamila Thompson and her husband James Walbourne, as well as other related musicians, including Walbourne's brother and Richard Thompson's son from his second marriage.
In July 2024, music from Proxy Music, an album of Thompson's music, was performed at London's Cadogan Hall, with Neil McCormick of The Daily Telegraph describing it as "more of an impromptu family shindig than a slickly presented show."