Singleton came through the Saracens Academy prior to joining Worcester Warriors in 2014.[1] In October 2016 he made his professional debut for Worcester away in Russia against Enisei-STM in the EPCR Challenge Cup. In what proved to be a markedly good first professional season at Worcester, Singleton made twenty appearances. His Premiership debut came against Northampton Saints in November 2016. Singleton's good form as a young player, saw him collect a 'Club's Young Player of the Season' award for the 2016–2017 campaign.[2]
After five years at Worcester, Singleton returned to Saracens in 2019.[3] On 11 March 2020, Singleton joined Gloucester on a season-long loan deal for the 2020–21 season after Saracens were relegated to the RFU Championship due to salary cap breaches.[1][4] It was later confirmed he would remain at Gloucester permanently from the 2021–22 season.[3][5]
On 29 November 2023, Singleton would join French giants Toulon in the Top 14 on loan for the remainder of the 2023-24 season. This would give Singleton more game time since recovering from a serious knee injury. He will return to Gloucester in the Premiership for the 2024-25 season.[6]
In May 2017 Singleton received his first call-up to the senior England squad by coach Eddie Jones and started in a non-cap game against the Barbarians.[11][12] He was a member of the squad on their tour of Argentina but remained on the bench for both tests.[13][14] He was also called up as injury cover during their 2018 tour of South Africa but did not participate in the series.[15]
On 11 August 2019, Singleton won his first cap for England off the bench against Wales at Twickenham in a warm-up match and the next day his selection for the 2019 Rugby World Cup was confirmed.[16][17] His only appearance at the tournament came as a replacement for Luke Cowan-Dickie during a pool stage fixture against the United States.[3][18]
Singleton was called up to the England squad on 15 November 2021 as cover for the injured Jamie George for the game against South Africa during the 2021 Autumn Nations Series.[19]