Aspects of chemistry content knowledge held by 265 UK-based pre-service teachers (PSTs) were probed using 28 diagnostic questions in five chemistry concept areas, "Particle theory and changes of state", "Mass conservation" (taught to 11-14-year-olds), and "Chemical bonding", "Mole calculations" and "Combustion reactions" (taught to 14-16-year-olds). Data were collected over six years from academically able science graduates starting a full-time, university-based teacher education programme of one academic year duration. PSTs in three sub-cohorts ("chemists", "physicists" and "biologists" on the basis of their undergraduate degrees) demonstrated similar levels of content knowledge (CK) for "Particle theory and changes of state" and "Mass conservation". Biologists demonstrated statistically significantly weaker understanding than chemists and physicists in "Chemical bonding", "Mole calculations" and "Combustion reactions". Forty-four "triads" each comprising one chemist, physicist and biologist, matched by academic and personal backgrounds, showed that chemists outperformed biologists and physicists in "Chemical bonding" and "Combustion reactions". The findings suggest that non-chemists' CK is insufficient for teaching these chemistry concepts in high schools, despite their possession of "good" Bachelor of Science degrees. These data have implications for science teacher education, including how best to prepare science graduates from diverse backgrounds for teaching specialist science subjects to 11-16-year-olds.