Cantwell began his career at Norwich City, joining the club at under-10 level in 2008 and making his first-team debut in January 2018. He made 129 appearances for Norwich over six seasons and had loan spells at Fortuna Sittard and AFC Bournemouth. He joined Rangers in January 2023.
Cantwell played youth international football for England at under-17 and under-21 levels.
Cantwell made his first start for Norwich City in the team's first round EFL Cup match against Stevenage on 14 August 2018.[9] He made his Norwich City league debut in September 2018 against Reading.[10] In December 2018, he scored his first senior goal in a 3–1 victory over Rotherham United.[11] He had his contract extended by Norwich at the end of the 2018–19 season, after the club exercised a one-year option.[12] On 17 August 2019, he assisted two Teemu Pukki goals, as Norwich beat Newcastle United 3–1.[13]
On 31 January 2022, Cantwell joined AFC Bournemouth on loan until the end of the season.[14] Bournemouth chose not to buy him at the end of his loan deal, and so he returned to Norwich. He signed a one-year contract extension with Norwich for the 2022–23 season.[15]
Rangers
On 23 January 2023, Cantwell joined Scottish Premiership club Rangers for an undisclosed fee.[16] He scored his first goal for the club on 18 March 2023 in a 4–2 win against Motherwell.[17] Cantwell scored the first goal of the game in a 3–0 victory over Celtic at Ibrox on 13 May 2023, rifling home a shot on the rebound after Joe Hart parried John Lundstram's initial long range effort.[18]
In his second season at Rangers, Cantwell continued to be a key player in midfield and in supporting the attack. On 24 January 2024, he scored the second goal of the game in a 3–0 away victory for Rangers against Hibernian.[19] On 3 February 2024, Cantwell scored the third goal of the game in a 3–0 victory over Livingston at Ibrox.[20] He scored his first goal for the club — a penalty — in a 1–0 home win over Leeds on 30 November 2024.[21]
Blackburn Rovers
On 30 August 2024, Blackburn Rovers announced the signing of Cantwell on a three-year deal for an undisclosed fee.[22]
On 30 August 2019, Cantwell was included in the England under-21 squad for the first time[26][27] and made his debut as a 61st-minute substitute for Morgan Gibbs-White during the 2021 U21 EURO 2–0 qualifying win over Kosovo at Hull City on 9 September 2019.[28] In March 2021, he was included in the England squad for the group stage matches of the 2021 UEFA European Under-21 Championship. He was a late call-up to replace Mason Greenwood, who was ruled out by injury.[29] Cantwell made four appearances in total for the under-21 team.[25]