This study explores the neurocognitive predictors of response to intervention with GraphoGame Rime (GG Rime), an adaptive software game designed to aid the learning of English phonics. A cohort of 398 children (aged 6–7 years) who had participated in a recent randomised controlled trial (RCT) of GG Rime in the United Kingdom were studied. Half were randomly assigned to play GG Rime and the other half were assigned to Business As Usual (BAU). A series of pretests were given prior to the intervention to all participants, designed to measure phonological awareness skills, executive function (EF) skills and the ability to synchronise finger tapping to a rhythmic beat. Rhythmic synchronisation has been linked to reading readiness and early reading attainment, and is related to phonological awareness. Individual differences prior to the intervention in all three types of measure were significantly associated with progression through the game. Gender was also important for progression through the game, with boys progressing significantly further than girls. Vocabulary was not a predictor of progression through the game. Playing time, rhythmic synchronisation, phonological skills and EF skills did not differ by gender. Once playing time and non-verbal cognitive ability were controlled, phonological awareness, EF, rhythmic synchronisation and gender all remained significant predictors of progression through the game. In further analyses comparing these predictors, their interactions and controlling for the autoregressor of prior responsiveness to phonics instruction, phoneme awareness and EF skills were the strongest unique predictors. Analyses with the whole cohort (analysing BAU and GG children independently) showed that all neurocognitive measures contributed to progress in reading and spelling over the school year. We conclude that individual differences in phonological skills and EF skills predict which children will benefit most from computer assisted reading interventions like GG Rime. Further, boys respond better to this computerised intervention than girls. Accordingly, to be maximally beneficial to poor readers, the supplementary use of GG Rime in addition to ongoing classroom literacy instruction could be especially targeted to boys, but should be accompanied by a focus on developing both oral phonological awareness and EF skills.