Rush has a medical condition called spondyloepiphyseal dysplasia congenita which affects his growth, resulting in dwarfism.
He played roles on CBeebies series Apple Tree House and CBBC's The Dumping Ground and had played Tiny Tim in versions of A Christmas Carol both on stage at The Old Vic in London in 2017 and 2018, and on-screen in a Steven Knight televised retelling of the Charles Dickens classic in 2019.
[5] Rush also had the role of Ollie in Daisy May Cooper’s BBC One comedy Am I Being Unreasonable?, in which he improvised lines as well as performing from a script.
[6] He received praise for his performance in the show, with Lucy Mangan writing in The Guardian, “What a gift they have in Rush, who has the comic chops and emotional range of an actor twice his age, and the kind of chemistry with Cooper that is an absolute joy to watch.
[9] In June 2023, it was announced that Rush would portray Morris Gibbons, UNIT's scientific advisor, in the fourteenth series of Doctor Who.