Educated at Christ's College, Cambridge, and ordained at Reims in 1585, he was captured on board ship at Littlehampton, Sussex, 19 April, 1586, with three other priests, Thomas Bramston, George Potter, and Edward James. All were sent up to London and committed to prison 27 April, 1586.
After the failure of the Spanish Armada, the English Government took severe measures against some of the Catholic priests in its custody. Crockett and James with two others, John Oven and Francis Edwardes, were selected for trial, which took place at Chichester on 30 September 1588. All were condemned to death, under 27 Eliz. c. 2, for being priests and coming into the realm; but Oven on taking the Oath of Supremacy was respited. The other three were drawn on one hurdle to Broyle Heath, near Chichester, where Edwardes recanted. Crockett ascended the scaffold and blessed the crowd in Latin whhich brought shouts of anger upon him, however he changed into praying in English whereupon the crowd cheered. James and Crockett faced their deaths without fear and were executed after absolving each other, safe in the knowledge of the righteousness of their beliefs.
Blessed Ralph Crockett's father Adam, in his later years entered the Church on the Continent and his descendants remained recusant continued to practise their Catholic Faith in the face of continued persecution. This branch of the originally Norman Crockett family remain largely Catholic to this day (2009); Blessed Ralph's descenants include Colonel Basil Crockett DSO, 1877-1939, Colonel 11th Regiment of Hampshires; John Crockett, 1918-1987, artist and film director; and Dr Antony Crockett, FRCGP 1956- , General Practicioner, medical author and asthma specialist.