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They were readmitted to England by Oliver Cromwell in 1657.
Catholicism.
Following The English Civil Wars of 1642 - 1651, England (and Scotland and Ireland separately) were ruled by Oliver Cromwell, his son Richard Cromwell and a pseudo parliamentary body known as The Council of State. The King, Charles I, had been executed for treason in 1649. Following a political crisis after the death of Oliver Cromwell in 1658, Charles I's son was invited to return as King and he became King Charles II in 1660. This was known as The Restoration of the Monarchy.
After Oliver Cromwell died, the English people no longer had a ruler or leader. They extended an invitation to Charles II, son of Charles I, to return to England as King. They did have conditions, Charles II could not change the national religion from protestant to catholic.
The period is called the Restoration because it marks the restoration of the English monarchy, specifically the return of King Charles II to the throne in 1660 after the period of Puritan rule under Oliver Cromwell. This event brought stability and a return to traditional forms of government and society in England.
Mary I (Bloody Mary).
To quote from Wikipedia "However, his measures against Catholics in Scotland and Ireland have been characterised as genocidal..." I do not believe the Cromwell ever let Catholics return to England and live.
Because of all the blood she shed to return England to Roman Catholicism
The objectives of the Spanish Armada were to overthrow Elizabeth I of England, return England to Catholicism, and stop English involvement in the Spanish Netherlands.
Oliver Cromwell (1599 - 1658) was an English soldier and statesman who helped make England a republic and then ruled as lord protector from 1653 to 1658. He executed King James I. His son Richard was named as his successor and was lord protector of England for 8 months. However, he was not a charismatic leader like his father and he could not reconcile the various political, military and religious factions of his day and soon lost the support of the army on which his power depended. Parliament therefore asked King James' son to return to England as the monarch.
Mary was a Catholic and was trying to return England to Catholicism after Henry VIII's reign.
There are two Monarchs known for trying to return England to Catholicism, Queen Mary I, who did bring the Church of England back into the Catholic Church, and King James II & VII who opened talks with the Pope to bring the Church of England back into the Catholic Church before he was over thrown in the Glorious Revolution. Also John Henry Cardinal Newman converted to Catholicism in the nineteenth century and did a wonderful job of explaining Catholicism to Anglicans.