The baby's due date is usually calculated at 40 weeks gestation - with anything from 37 to 42 weeks being considered 'normal'.
Generally at about 40 weeks, if there is no sign of labour, the mother will start to get nonstress tests every few days. Nonstress tests are where, among other things, a fetal monitor is attached to the mother to ensure that the baby is not under stress. And even if the nonstress tests show that the baby is not under stress in the womb, most doctors will attempt to induce labour at an estimated gestational age of 42 weeks.
ETA: This means that if the due date is indeed, 'mid-July' - the Cambridge baby will statistically most likely to be born on a day in July.