On 23rd March 2018, Norwich City announced their first Summer 2018 signing after coming to terms with Dagenham & Redbridge for City to sign their 21 year old striker. Bloomfield came through the Daggers' academy and made a League Two appearance whilst aged 17. He later had loan spells at Chatham Town, Erith & Belvedere, Maldon & Tiptree, Chelmsford City, Billericay Town, Grays, Witham Town, Brentwood and Aveley (twice)before returning to the Dagenham first team. he made 28 appearances for Dagenham scoring three goals.
On 25th June 2018, it was announced that Bloomfield would be joining Scottish side Hamilton on loan for the 2018/19 season following in the footsteps of Remi Matthews and Carlton Morris.