Investigators at the Centre for Research on the Wider Benefits of Learning at London's Institute of Education have been tracking the wellbeing and test results of 2,000 children aged 7 to 11.
They found that 10-year-olds had, on average, a 22 per cent chance of becoming victims.
Once other factors such as gender, background and early behaviour had been subtracted, a strong difference was noticeable between those who had gained the top grade (level 3) in key stage 1 English tests and those who gained the lowest.
Girls with high scores had just a 6 per cent chance of being victimised at age 10, while the figure was 11 per cent for the bottom group. For boys it was 10 per cent for high-achievers and 15 per cent for low-scorers.
Boys and girls with lower English scores were also more likely to become bullies, the study found.
Dr Leslie Gutman, who led the government-funded research, said: "Proficiency in English is related to communication skills and it is those that are important for good peer relationships. It's not just about doing well in school. The test scores act as a proxy for wider social skills."
The study, Children's Wellbeing in Primary School: Pupil and School Effects, found that, overall, children's social behaviour improved between the ages of 8 and 10. But a fifth of pupils suffered declining or low levels of wellbeing.
Although a link was found between happiness and academic achievement, the benefits of a middle-class background outweighed the advantages of wellbeing.