Tom Skinner was born in London on January 26, 1980, and began playing drums at the age of nine. He first liked 1990s grunge and metal bands such as Napalm Death, then found experimental jazz through John Zorn and Ornette Coleman. Between 1993 and 1996 he attended workshops at the Weekend Arts College in London, and by 1998 he was working in the city's jazz community: with a Tomorrow's Warriors group led by Gary Crosby (alongside Soweto Kinch, Dave Okumu, Andrew McCormack and Tom Herbert) and with the Denys Baptiste Quartet. He graduated from the Tomorrow's Warriors programme in 2001. His first records as a sideman include Baptiste's Alternating Currents (Dune, 2001), saxophonist Ingrid Laubrock's Some Times (Candid, 2001) and Forensic (F-IRE, 2004), Byron Wallen's Indigo (Twilight Jaguar, 2002) and Finn Peters's Su-Ling (Babel, 2006). He also played with the singer Cleveland Watkiss and the saxophonist Martin Speake, and the German edition of Wikipedia lists Jean Toussaint, Branford Marsalis and Stanley Turrentine among those he has worked with.

From the mid-2000s he co-led his own groups. Jade Fox, a trio with the guitarist Dave Okumu and the bassist Tom Herbert, released the twelve-inch Down Below on Traficante in December 2004. In 2007 he and Shabaka Hutchings founded the trio Zed-U with Neil Charles, whose album Night Time on the Middle Passage appeared on Babel in 2009. He was also a member of the London and Nairobi dance band Owiny Sigoma Band, whose debut came out on Gilles Peterson's Brownswood label in May 2011, and of the soul group Elmore Judd. Under the name Hello Skinny he released a self-produced solo album on Slowfoot in 2012, the Revolutions EP in 2013 and Watermelon Sun on Brownswood in 2017, records that range from experimental jazz to electronics and dance music.

In 2011 Skinner and Shabaka Hutchings founded Sons of Kemet, a quartet of saxophone and clarinet, tuba and two drummers. The first lineup paired Skinner with the drummer Seb Rochford and the tubist Oren Marshall; Theon Cross took over the tuba chair after the debut. Burn came out on Naim Jazz on September 9, 2013, and the band won Best Jazz Act at that year's MOBO Awards. Lest We Forget What We Came Here to Do followed on Naim on September 25, 2015. In 2018 the group became the first British act signed to Impulse!, and its third album, Your Queen Is a Reptile (March 30, 2018), was nominated for the Mercury Prize. Eddie Hick replaced Rochford for the fourth and last album, Black to the Future (May 14, 2021). In June 2022 the band announced that it was closing its chapter for the foreseeable future; Skinner told All About Jazz that after ten years the members wanted room for separate projects, and that he saw the break as not necessarily final.

Alongside Sons of Kemet he kept a trio with the saxophonist Idris Rahman and the bassist Leon Brichard, Wildflower, which released three albums between 2017 and 2021, and a second trio with Okumu and Herbert whose live album Undone: Live at the Crypt appeared on The Vinyl Factory in 2019. He played drums on a track of Jonny Greenwood's score for The Master (2012) and on Floating Points's Elaenia (2015). In December 2020 he was one of twelve musicians who recorded London Brew, an improvised set inspired by Miles Davis's Bitches Brew, released by Concord Jazz on March 31, 2023. In 2021 he joined Greenwood and the Radiohead singer Thom Yorke to form the Smile, a rock band whose debut was streamed from Glastonbury in May 2021. It has made three albums on XL Recordings: A Light for Attracting Attention (May 13, 2022), Wall of Eyes (January 26, 2024) and Cutouts (October 4, 2024). He also plays drums on Beth Orton's Weather Alive (2022) and on Alabaster DePlume's Gold (2022) and Come with Fierce Grace (2023).

His first album under his own name, Voices of Bishara, grew out of a "Played Twice" evening at Brilliant Corners in Hackney in early 2018, where he reworked Tony Williams's Life Time with the same five players who later made the record. At the end of 2018 he recorded new music with them in one room: Shabaka Hutchings and Nubya Garcia on tenor saxophones (Hutchings also on bass clarinet, Garcia also on flute), Kareem Dayes on cello and Tom Herbert on bass. He then spent the pandemic chopping and looping the takes, brought in the engineer Dilip Harris for the final mix, and released the album on November 4, 2022 through International Anthem, Nonesuch and Brownswood. The title nods to the label of the cellist Abdul Wadud, whose 1978 solo record By Myself Skinner had come to treasure. Voices of Bishara Live at "Mu", recorded in London on January 18 and 19, 2023 with the saxophonists Robert Stillman and Chelsea Carmichael, was issued on International Anthem on May 10, 2024. His second studio album, Kaleidoscopic Visions, came out on Brownswood and International Anthem on September 26, 2025; it is built from fully composed pieces, and he plays drums, percussion, vibraphone, guitars, synthesizer and piano on it, with guests including Me'Shell Ndegéocello and the guitarist Adrian Utley. His own site describes him in 2025 as a lifelong Londoner and as two decades into a career at the center of London's jazz community.

Skinner is a drummer who works in the space between free improvisation, Afro-Caribbean and African grooves, and electronic editing, and NPR has praised his habit of sitting at the pivot between chaos and clarity. His earliest listening ran from grunge to John Zorn and Ornette Coleman; he has named the cellist Abdul Wadud, whose solo album By Myself shaped Voices of Bishara, and Tony Williams's Life Time as direct starting points, and he has said that he took his cue for the album's cut-and-loop editing from disco re-edits. The Guardian placed that album's mood between the beat-splicing of Makaya McCraven and Don Cherry's spiritual melodies, and All About Jazz ranked it among the best jazz records of 2022. In Sons of Kemet he was half of a two-drummer front line behind Shabaka Hutchings and a tuba, an arrangement that put rhythm at the center of the music. His recent public profile also owes much to the Smile, a rock band with two members of Radiohead; that work sits outside jazz, but his own records, Sons of Kemet and London Brew do not, and the German and Dutch editions of Wikipedia describe him as a jazz drummer.