[23][24] He made eight appearances in 2006–07,[25] and when first-choice goalkeeper Andy Oakes was sent off in the opening match of 2007–08, Stockdale took over and became manager Dave Penney's preferred choice in goal.

[28] Stockdale was scouted by Premier League clubs including Birmingham City and Newcastle United before,[29] in April 2008, Darlington accepted a bid from Fulham.

[40] He played for Leicester as their promotion to the Championship as League One champions was confirmed after a 2–0 victory over Southend United,[41] after which he said he would be interested in joining the club for the following season.

[47] Due to Mark Schwarzer being injured in pre-season and being linked with a move to Arsenal, Stockdale was the first-choice goalkeeper at Fulham at the start of the 2010–11 season.

[48] He started the season by keeping a clean sheet at Bolton Wanderers, and followed up by saving a penalty kick at Craven Cottage against Manchester United in a 2–2 draw on 22 August.

[49][50] He continued his run in the team in January due to Schwarzer's participation in the AFC Asian Cup, starting with West Bromwich Albion where he kept a clean sheet.

[49] In June 2011, new Fulham manager Martin Jol said he wanted to loan Stockdale out to get a regular run of matches, but had no intention of selling the player.

[53][54] Swansea had a £2 million bid rejected on 11 July,[55] and Stockdale tweeted that he would "love to help [his] hometown club back to where they belong" if a move to Leeds became an option.

[57] On 26 July 2011, Stockdale signed a new four-year contract with Fulham and subsequently went out on a one-year loan to Championship club Ipswich Town.

[63] Stockdale returned to Hull on 18 January 2013 on loan for what remained of the season,[64] and made 19 appearances[62] as the team earned promotion to the Premier League as Championship runners-up.

[66] He made his debut on 9 August, the opening day of the season, in a 1–0 defeat against Sheffield Wednesday, and appeared in 42 league matches as Albion finished 20th in the table.

[67][68] He was active in his support for the families of victims of the 2015 Shoreham Airshow crash, which led to his being named as Brighton & Hove Albion's PFA Community Champion.

[71] Stockdale made 45 appearances in 2016–17,[72] saving a Stefan Johansen penalty in a 2–1 win over his former club Fulham,[73] and keeping 20 clean sheets as Brighton were promoted to the Premier League.

[79] He went straight into the starting eleven for the opening fixture of the 2017–18 season, which Birmingham lost 1–0 away to Ipswich Town,[80] and kept his place until he injured his wrist in mid September.

[83] He made what the Daily Telegraph reporter dubbed a magnificent save from Fulham's Aleksandar Mitrović in the final game of the season to help Birmingham avoid relegation and end their opponents' 23-match unbeaten run.

[85] He made his debut the same day, starting in their 3–2 home defeat to Peterborough United,[86] and played three matches before Southend's main goalkeeper, Mark Oxley, returned from suspension.

[87] Stockdale joined another League One club, Wycombe Wanderers, on 22 November on a seven-day emergency loan, due to injuries to both first- and second-choice keepers, Ryan Allsop and Yves Ma-Kalambay.

[92] He played in Birmingham's 3–0 defeat away to Portsmouth in August 2019, when manager Pep Clotet fielded a shadow squad,[93] but the starting spot in league matches was shared by Lee Camp and Connal Trueman.

[94] After Wycombe Wanderers' second-choice goalkeeper, Cameron Yates, was injured in training, Stockdale returned to the club on 24 January 2020 on loan until the end of the season.

[95] He was an unused substitute in Wycombe's 2–1 win over Oxford in the 2020 League One play-off final at Wembley, as the club was promoted to the Championship for the first time.

[100] Having not played first-team football in over a year,[99][101] Stockdale joined League Two club Stevenage on an emergency two-week loan deal on 2 February 2021, providing temporary cover for the injured Jamie Cumming.

[105] In the final appearance of the two-week agreement,[101] Stockdale saved a 90th-minute penalty to help Stevenage record a 1–0 victory at Crawley Town;[106] again being named in the EFL League Two 'Team of the Week'.

[119] He was included in the 25-man squad for England for the match against Denmark in February 2011 after impressing manager Fabio Capello with his calmness standing in for Schwarzer at Fulham.