Cullen was first included in a West Ham matchday squad for their Premier League fixture against Arsenal at the Emirates Stadium on 14 March 2015, remaining an unused substitute as they lost 3–0. He was also called up and unused on 9 May, as West Ham lost 1–0 at Aston Villa. On 2 July 2015, he made his first-team debut for the club in a 3–0 home victory over Lusitanos of Andorra in the UEFA Europa Leaguefirst qualifying round first leg, replacing Joey O'Brien after 60 minutes; he started in their 1–0 victory in the second leg a week later, making way for Amos Nasha after 63 minutes. With manager Slaven Bilić putting priority on the team's Premier League performance, he made an array of changes for their third qualifying round second leg away to FC Astra Giurgiu on 6 August, including starting Cullen in his first competitive match against a professional opponent. Twenty-three days later he made his Premier League debut, replacing Diafra Sakho at the end of a 3–0 win over Liverpool at Anfield. Cullen returned from loan at Bolton Wanderers in January 2018 making an appearance in the FA Cup away at Shrewsbury Town. He was praised for his performance by West Ham manager, David Moyes, in a poor performance by West Ham which ended 0–0. Cullen also had two front teeth kicked-out accidentally by Shrewsbury player Abu Ogogo.
He signed on loan for Bradford City in February 2016. In March 2016 his loan was extended until the end of the 2015–16 season. On 8 August 2016, Cullen re-signed for Bradford City on a five-month loan deal. He scored his first league goal for the club in the 2–1 victory at MK Dons on 16 August 2016. His loan at the club was extended on 3 January 2017 until the end of the season.
Loan to Bolton Wanderers
On 1 August 2017, Cullen, along with West Ham teammate Reece Burke, joined Bolton Wanderers on loan until the following January.
On 30 August 2018, Cullen joined Charlton Athletic on loan until the end of the 2018–19 season. Cullen dislocated his shoulder on 6 November 2018 playing against Walsall, leaving the pitch in the 80th minute. He returned to the first team in January 2019 against Accrington Stanley. On 26 May 2019, Cullen played the full 90 minutes of the League 1 Play Off final as Charlton won 2–1 to return to the Championship. Having spent the season on-loan, Cullen returned to West Ham and played in several pre 2019–20 season friendlies. In August 2019, he returned to Charlton on-loan for the 2019–20 season.
