Born in Winchester, England, Cargill grew up as a Southampton fan and even had a season ticket for the club. After spells at the academies of Leicester City and Southampton (in which he stayed on for two years), Cargill joined AFC Bournemouth's youth ranks, which Cargill stated he joined the club's U13 academy and turned professional in 2012. After a loan spell with A.F.C. Totton and Welling, Cargill signed his first professional contract on a one-year contract in April 2013.
After making an impressive display in the pre-season friendly and his loan spell at Welling at the first half of the 2013–14 season, Cargill signed a two-year and a half contract, keeping him until 2016.
In effort of making a first team breakthrough ahead of the 2014–15 season, Cargill made his first senior appearance for Bournemouth on 12 August 2014 as a centre-back in a 2–0 League Cup win at Exeter City, and the following week he was rewarded with a place on the bench in Bournemouth's 2–1 defeat to Nottingham Forest in the Championship. The defender retained his place for the next round of the League Cup on 26 August as Bournemouth beat Northampton Town 3–0, and also played in the third round 3–0 victory at Cardiff City on 23 September and the Cherries' 2–1 win over West Bromwich Albion in the fourth round on 28 October. His impressive display earned him a contract extension, keeping him until 2017.
Then, Cargill started in the match against Liverpool in the fifth round of the Football League Cup, which Bournemouth lost 3–1. During the match, Cargill unintentionally made headlines after having a wig, which "fell off his head, and onto the pitch". One of his teammates, Harry Arter came to his defense after he believed that The Independent wrote an article about Cargill and accused the newspaper "bullying".
In November 2012 he was loaned to Southern League club AFC Totton on a one-month deal as part of a work experience arrangement. The loan was later extended until the end of the season. Cargill made his Totton debut in a 2–1 defeat to Forest Green Rovers in the FA Trophy. At Totton, Cargill cemented himself as a first-team regular, scoring 3 goals in 26 appearances and being voted the Fans' Player of the Season. Cargill later credited Totton with helping to make him the player he is today.
On 4 October 2013, Cargill joined Welling United on a one-month loan until 2 November 2013. Cargill made his Welling United debut the next day, in a 1–1 draw against Barnet. Cargill loan spell with Welling United was soon extended until 29 December 2013. Once again, Cargill was extended further until 22 January 2014. After his loan spell with Welling United came to an end with thirteen appearance, Cargill said his time at Welling United helped him with confidence.
At the end of the 2013–14 season Chris Hargreaves, having recently moved from a coaching role at Bournemouth's academy to become manager of Torquay United, signed Cargill on loan to play at left-back. Cargill made his Torquay United debut, in a 2–1 win over Bristol Rovers. Cargill then provided assist for Ashley Yeoman, in a 2–1 win over Exeter City on 21 April 2014, in hope of survival relegation. However, the pair were unable to prevent the Gulls' relegation to the Conference, as Cargill made five appearance for the club.
On 1 February 2016, Cargill joined Coventry City on loan until the end of the season. At Coventry he scored once; his goal coming in a 6-0 win over Bury.
In August 2016 he joined Gillingham on loan. At Gillingham he scored his first and only goal in a 1-1 draw with Peterborough United.
In August 2017 he joined Fleetwood Town on loan. He scored his first goal for Fleetwood in an EFL Trophy tie against Leicester City Under-23s on 29 August 2017.
On 6 November 2014, Cargill was called into the England youth set up for the first time, being named in the England U20 squad for matches against Portugal and Canada. He started the Canada game and capped a dream debut by scoring a goal, which he described as the "best feeling".As of match played 12 September 2017