In March 2017, Swindells was cast to replace Joe Alwyn as Donald in The Vanishing, a Scottish psychological thriller film directed by Kristoffer Nyholm, starring Gerard Butler and Peter Mullan.

[8] Swindells also starred as Adam in the 2018 drama film VS.[9] In 2019 Swindells began starring alongside Ncuti Gatwa, Emma Mackey, Asa Butterfield, and Gillian Anderson in the Netflix comedy-drama series Sex Education as Adam Groff, the headmaster's son, initially a bully who has a tense relationship with his father.

Swindells appeared in the films Emma (2020) and Barbarians (2021), and played Simon Hadlow in the 2021 BBC One crime drama Vigil led by Suranne Jones.

The following year, he began starring in the lead role of David Stirling in the World War II series SAS: Rogue Heroes, also on BBC One.

Swindells appeared in Greta Gerwig's Barbie, reuniting with his Sex Education co-stars Ncuti Gatwa and Emma Mackey.