After progressing through Swansea City's Academy, Cornell was included in Swansea's senior squad for their 2008 pre-season tour of Spain. However the 17-year old's progress was halted when he suffered a serious wrist injury on tour. Later that season, Cornell was called up to the first team bench for Swansea's fifth round FA Cup match against Fulham after loan signing Dimitrios Konstantopoulos was unable to extend his stay at the club. Ten days later, Cornell was included again on Swansea's bench for the Swans FA Cup fifth round replay against Fulham. After impressing manager Roberto Martínez, Cornell was installed as Dorus de Vries' understudy for the rest of the 2008–09 season but made no further appearances in Swansea's remaining matchday squads. Cornell made his professional debut for Swansea on 25 August 2009 when he was named in the starting line-up for the League Cup match against Scunthorpe United. In February 2010, Cornell signed a new three-and-a-half year contract with Swansea to keep him at the club until July 2013. The 2009–10 season saw Cornell included on the bench for 45 of Swansea's 46 Football League Championship games. Following loan spells at Port Talbot Town and Hereford United, Cornell returned to Swansea for the 2012–13 season as third choice goalkeeper. In September 2012, Cornell signed a new three-year deal, keeping him at the club until July 2015. Due to injuries to Michel Vorm and Gerhard Tremmel, Cornell was included on the bench on 14 occasions for Swansea during the season. On 28 May 2015 Swansea City confirmed that Cornell had been released from the club.
Port Talbot Town (loan)
In the 2010–11 season, Cornell fell down the pecking order at Swansea following the signing of Yves Ma-Kalambay as cover for Dorus de Vries and was loaned out to Welsh Premier League side Port Talbot Town during the second half of the season to gain first team experience. Cornell made 14 appearances for Port Talbot, keeping 5 clean sheets.
Hereford United (loan)
After Swansea's promotion to the Premier League, Cornell's opportunities were further limited. In August 2011 Football League Two side Hereford United signed Cornell on an initial one-month loan deal as cover for Adam Bartlett. After some impressive performances, Cornell's loan was extended by Hereford until the end of the 2011–12 season. Cornell made 27 appearances in all competitions for Hereford.
On 1 July 2013, Cornell joined St Mirren on a season-long loan. Cornell made 6 appearances in all competitions for St Mirren before his loan was cancelled in December 2013.
Following his release from Swansea City, Cornell joined League One team Oldham Athletic in July 2015 on a one-year contract with the option of a second.
Northampton Town
In June 2016 Cornell joined Northampton Town on a two-year contract. He was offered a new contract by Northampton at the end of the 2017–18 season, following their relegation.
