In March 2009, Hudson-Odoi signed for Grays Athletic on an initial one-month loan with a view to a permanent deal after spending two weeks on trial with the Conference National club.[9] He made his debut on 7 March 2009 in the 2–1 home win over Altrincham, supplying Jamie Slabber with a cross to score Grays' second goal.[10] He joined Histon on a contract until January 2010 in August 2009.[11] He rejoined Grays on a month's loan on 27 November.[12] He rejoined Grays Athletic for a third time on 26 October 2010, before joining Conference South club Thurrock in December. After a stint abroad at Hungarian side Vasas, Bradley joined Metropolitan Police on trial, before signing a contract in January 2014.[13] Playing for Wealdstone in the 2015–16 season, Bradley was voted their player of the season. After the season ended, Wealdstone announced Bradley's departure for a team in the National League,[14] later announced as Sutton United.[15]
Hudson-Odoi made his first league appearance for Sutton as a substitute on their opening day defeat of the 2016–17 season to Solihull Moors on 6 August 2016, coming on for Roarie Deacon, before making his first full appearance and debut in a 2–0 win over Torquay United on 16 August. On his third appearance for Sutton, he scored his first league goal for the club and the winner in a 1–0 home victory over Dagenham & Redbridge on 29 August 2016 when he connected with Ross Stearn's cross and struck a half volley 11 minutes into the game.[16] On 10 November 2016 Hudson-Odoi joined Maidstone United on loan for one month.[17]
Hudson-Odoi appeared in Sutton's historic run to the fifth round of the FA Cup for the first time ever, including a 3–1 victory over League One side and local rivals AFC Wimbledon in the third round on 17 January 2017,[18] and a 2–0 defeat to Premier League team Arsenal in the fifth round on 20 February.[19] On 23 February 2018, he was released by Sutton and signed for Hampton & Richmond Borough. On 22 May 2018, Hudson-Odoi returned to Wealdstone.[20] On 25 January 2019, Hudson-Odoi left Wealdstone after an injury hit season[21] and soon reunited with former manager, Alan Dowson at fellow National League South side, Woking.[22] However, just after featuring twice for the Surrey-based side, Hudson-Odoi opted to leave the club in February 2019.[23]