The mother of two was shot and stabbed one week before the EU referendum.
Cox died on June 16 after being shot and stabbed outside a library in her constituency.
Thomas Mair, 52, is accused of shooting and stabbing Cox in the street.
Witnesses said a man shot at Cox with what looked like an "old" or "makeshift" gun.
The 52-year-old had a history of mental illness, his brother said.