Swift has represented England from U16 through to U21 level. He made his international debut in a Victory Shield defeat to Wales U16 on 15 October 2010. He was part of the U17 squad which won the 2011 FA International Tournament and the 2012 Algarve Tournament, but he could not help the team to qualify for the 2012 European U17 Championship. Swift made 9 appearances during the U19s' failed qualification attempts for the 2013 and 2014 European U19 Championships. Moving up to U20 level for the 2014–15 season, Swift was a part of the squad which won the 2014 Four Nation Tournament and he finally scored his first international goal with the opener in a 2–1 victory over United States U20 on 29 March 2015. Swift was called into the U20 squad for the 2015 Toulon Tournament and appeared in all of England's matches as the Young Lions finished fourth. In November 2015, Swift made his U21 debut with a start in a 3–1 2017 European U21 Championship qualifying win over Switzerland. On 25 August 2016 he was called up for Gareth Southgate's U21 side to face Norway in a UEFA U21 Euro 2017 qualifier.