From the Act of Supremacy in 1558 when Elizabeth ascended the throne to 1570 there were no Catholic martyrs for the faith. But the English crown shifted their modus operandi after Pope Pius V's bull Regnans in Excelsis which excommunicated Elizabeth, the English crown began to crack down. Five Catholics were slain for treason for plotting to overthrow the sovereign.
However, there were a slew of anti-Catholic laws which were promulgated. In 1571, the English Crown denied the Holy See any jurisdiction, publishing anything from the Pope, forbidding "poperies" like crosses, rosaries and Agnus Dei from the the pope.
Elizabeth also commanded that the Book of Common prayer be used in all churches. Later, it became punishable to not attend Church of England services, draw anyone away from the state religion, teach without the blessing of an Anglican bishop or even celebrate the Catholic Mass. In 1585, it became a capital crime to go abroad to be ordained as a Catholic priest.
One could rightly point to the 283 Protestants who were killed for their faith under Mary I were also martyred for their faith, during an unfortunate era of intolerance in Christendom. May we now remember to have unity on essential thing, liberty on dubious things and charity for all.