Born in Watford, Cottrell joined the academy of Premier League club Arsenal on 3 June 2010, at the age of eight.[2] He progressed through the club's Hale End academy, where his performances drew interest from German and French sides, Borussia Dortmund and Marseille, respectively.[3] He signed his first professional contract with the club in July 2019.[4]
Cottrell made his unofficial debut in Arsenal's 4–1 pre-season friendly win against Milton Keynes Dons; coming on as a second-half substitute for Kieran Tierney, he impressed in an unnatural left wing-back position.[5] Later in the same season, he was included in Arsenal's senior squad ahead of a UEFA Europa League fixture against Norwegian opposition Molde, alongside fellow academy graduate Miguel Azeez.[6] Despite not featuring in Arsenal's 3–0 win, he remained on manager Mikel Arteta's radar, and made his professional debut in Arsenal's 4–2 win against Irish side Dundalk on 10 December 2020, coming on as a second-half substitute for Emile Smith Rowe.[7][8]
Having been ruled out for most of the 2021–22 season, only playing in two games, he returned to regular action the following year, but found first-team opportunities limited, despite impressing in the Premier League 2.[9]
In August 2023, he completed a permanent transfer to Slovenian side Mura, becoming the first Englishman to play for the club.[8][10][11]
On 9 December 2024, Cottrell joined Slovak First Football League club Zemplín Michalovce on a two-and-a-half year deal, once again becoming the first Englishman to represent the club.[12] He scored his first goal for Zemplín in a 4:2 loss against MFK Skalica.[13]